11X1 t05 03 combinations

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CombinationsCombinationsA combination is a set of objects where the order that they are arranged is not important.CombinationsA combination is a set of objects where the order that they are arranged is not important.If we arrange objects in a line, and the order is not important then;CombinationsA combination is a set of objects where the order that they are arranged is not important.If we arrange objects in a line, and the order is not important then;A B is the same arrangement as B ACombinationsA combination is a set of objects where the order that they are arranged is not important.If we arrange objects in a line, and the order is not important then;A B is the same arrangement as B Ae.g. 5 objects, arrange 2 of themCombinationsA combination is a set of objects where the order that they are arranged is not important.If we arrange objects in a line, and the order is not important then;A B is the same arrangement as B Ae.g. 5 objects, arrange 2 of themA B B A C A D A E AA C B C C B D B E BA D B D C D D C E CA E B E C E D E E DCombinationsA combination is a set of objects where the order that they are arranged is not important.If we arrange objects in a line, and the order is not important then;A B is the same arrangement as B Ae.g. 5 objects, arrange 2 of themA B B A C A D A E AA C B C C B D B E BA D B D C D D C E CA E B E C E D E E D20 nsPermutatio 25 PCombinationsA combination is a set of objects where the order that they are arranged is not important.If we arrange objects in a line, and the order is not important then;A B is the same arrangement as B Ae.g. 5 objects, arrange 2 of themA B B A C A D A E AA C B C C B D B E BA D B D C D D C E CA E B E C E D E E D20 nsPermutatio 25 PCombinationsA combination is a set of objects where the order that they are arranged is not important.If we arrange objects in a line, and the order is not important then;A B is the same arrangement as B Ae.g. 5 objects, arrange 2 of themA B B A C A D A E AA C B C C B D B E BA D B D C D D C E CA E B E C E D E E D20 nsPermutatio 25 P10!220 nsCombinatio5 objects, arrange 3 of them5 objects, arrange 3 of themA B C B A C C A B D A B E A BA B D B A D C A D D A C E A CA B E B A E C A E D A E E A DA C B B C A C B A D B A E B AA C D B C D C B D D B C E B CA C E B C E C B E D B E E B DA D B B D A C D A D C A E C AA D C B D C C D B D C B E C BA D E B D E C D E D C E E C DA E B B E A C E A D E A E D AA E C B E C C E B D E B E D BA E D B E D C E D D E C E D C5 objects, arrange 3 of themA B C B A C C A B D A B E A BA B D B A D C A D D A C E A CA B E B A E C A E D A E E A DA C B B C A C B A D B A E B AA C D B C D C B D D B C E B CA C E B C E C B E D B E E B DA D B B D A C D A D C A E C AA D C B D C C D B D C B E C BA D E B D E C D E D C E E C DA E B B E A C E A D E A E D AA E C B E C C E B D E B E D BA E D B E D C E D D E C E D C60 nsPermutatio 35 P5 objects, arrange 3 of themA B C B A C C A B D A B E A BA B D B A D C A D D A C E A CA B E B A E C A E D A E E A DA C B B C A C B A D B A E B AA C D B C D C B D D B C E B CA C E B C E C B E D B E E B DA D B B D A C D A D C A E C AA D C B D C C D B D C B E C BA D E B D E C D E D C E E C DA E B B E A C E A D E A E D AA E C B E C C E B D E B E D BA E D B E D C E D D E C E D C60 nsPermutatio 35 P5 objects, arrange 3 of themA B C B A C C A B D A B E A BA B D B A D C A D D A C E A CA B E B A E C A E D A E E A DA C B B C A C B A D B A E B AA C D B C D C B D D B C E B CA C E B C E C B E D B E E B DA D B B D A C D A D C A E C AA D C B D C C D B D C B E C BA D E B D E C D E D C E E C DA E B B E A C E A D E A E D AA E C B E C C E B D E B E D BA E D B E D C E D D E C E D C60 nsPermutatio 35 P10!360 nsCombinatioIf we have n different objects, and we arrange k of them and are not concerned about the order;If we have n different objects, and we arrange k of them and are not concerned about the order;! tsArrangemen ofNumber kPknIf we have n different objects, and we arrange k of them and are not concerned about the order;! tsArrangemen ofNumber kPkn !!!kknnIf we have n different objects, and we arrange k of them and are not concerned about the order;! tsArrangemen ofNumber kPkn !!!kknnknC If we have n different objects, and we arrange k of them and are not concerned about the order;! tsArrangemen ofNumber kPkn !!!kknnknC e.g. (i) How many ways can 6 numbers be chosen from 45 numbers?If we have n different objects, and we arrange k of them and are not concerned about the order;! tsArrangemen ofNumber kPkn !!!kknnknC e.g. (i) How many ways can 6 numbers be chosen from 45 numbers?456Ways CIf we have n different objects, and we arrange k of them and are not concerned about the order;! tsArrangemen ofNumber kPkn !!!kknnknC e.g. (i) How many ways can 6 numbers be chosen from 45 numbers?456Ways C8145060If we have n different objects, and we arrange k of them and are not concerned about the order;! tsArrangemen ofNumber kPkn !!!kknnknC e.g. (i) How many ways can 6 numbers be chosen from 45 numbers?456Ways C8145060Note: at 40 cents per game, $3 258 024 = amount of money you have to spend to guarantee a win in Lotto.(ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?(ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?511 Committees C(ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?511 Committees C With no restrictions, choose 5 peoplefrom 11, gender does not matter (ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?511 Committees C With no restrictions, choose 5 peoplefrom 11, gender does not matter 462(ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?511 Committees C With no restrictions, choose 5 peoplefrom 11, gender does not matter 462b) the committee contains only males?(ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?511 Committees C With no restrictions, choose 5 peoplefrom 11, gender does not matter 462b) the committee contains only males?57 Committees C(ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?511 Committees C With no restrictions, choose 5 peoplefrom 11, gender does not matter 462b) the committee contains only males?57 Committees C By restricting it to only males, there is only 7 people to choose from(ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?511 Committees C With no restrictions, choose 5 peoplefrom 11, gender does not matter 462b) the committee contains only males?57 Committees C21By restricting it to only males, there is only 7 people to choose from(ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?511 Committees C With no restrictions, choose 5 peoplefrom 11, gender does not matter 462b) the committee contains only males?57 Committees C21By restricting it to only males, there is only 7 people to choose fromc) the committee contains at least one woman?(ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?511 Committees C With no restrictions, choose 5 peoplefrom 11, gender does not matter 462b) the committee contains only males?57 Committees C21By restricting it to only males, there is only 7 people to choose fromc) the committee contains at least one woman?21462 Committees (ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?511 Committees C With no restrictions, choose 5 peoplefrom 11, gender does not matter 462b) the committee contains only males?57 Committees C21By restricting it to only males, there is only 7 people to choose fromc) the committee contains at least one woman?21462 Committees easier to work out male only and subtract from total number of committees(ii) Committees of five people are to be obtained from a group of seven men and four women.How many committees are possible if;a) there are no restrictions?511 Committees C With no restrictions, choose 5 peoplefrom 11, gender does not matter 462b) the committee contains only males?57 Committees C21By restricting it to only males, there is only 7 people to choose fromc) the committee contains at least one woman?21462 Committees 441easier to work out male only and subtract from total number of committees(iii) A hand of five cards is dealt from a regular pack of fifty two cards.a) What is the number of possible hands?(iii) A hand of five cards is dealt from a regular pack of fifty two cards.a) What is the number of possible hands?552 Hands C(iii) A hand of five cards is dealt from a regular pack of fifty two cards.a) What is the number of possible hands?552 Hands C2598960(iii) A hand of five cards is dealt from a regular pack of fifty two cards.a) What is the number of possible hands?552 Hands C2598960b) What is the probability of getting three of a kind?(iii) A hand of five cards is dealt from a regular pack of fifty two cards.a) What is the number of possible hands?552 Hands C2598960b) What is the probability of getting three of a kind?113 Hands Ckind" a ofthree"hasnumber which choose(iii) A hand of five cards is dealt from a regular pack of fifty two cards.a) What is the number of possible hands?552 Hands C2598960b) What is the probability of getting three of a kind?113 Hands Ckind" a ofthree"hasnumber which choose34Ccardsthoseof threechoose(iii) A hand of five cards is dealt from a regular pack of fifty two cards.a) What is the number of possible hands?552 Hands C2598960b) What is the probability of getting three of a kind?113 Hands Ckind" a ofthree"hasnumber which choose34C 248Ccardsthoseof threechooserestthefromcardstworemainingchoose(iii) A hand of five cards is dealt from a regular pack of fifty two cards.a) What is the number of possible hands?552 Hands C2598960b) What is the probability of getting three of a kind?113 Hands Ckind" a ofthree"hasnumber which choose34C 248Ccardsthoseof threechooserestthefromcardstworemainingchoose58656(iii) A hand of five cards is dealt from a regular pack of fifty two cards.a) What is the number of possible hands?552 Hands C2598960b) What is the probability of getting three of a kind?113 Hands Ckind" a ofthree"hasnumber which choose34C 248Ccardsthoseof threechooserestthefromcardstworemainingchoose58656 259896058656kind a of three P(iii) A hand of five cards is dealt from a regular pack of fifty two cards.a) What is the number of possible hands?552 Hands C2598960b) What is the probability of getting three of a kind?113 Hands Ckind" a ofthree"hasnumber which choose34C 248Ccardsthoseof threechooserestthefromcardstworemainingchoose58656 259896058656kind a of three P291594(iii) A hand of five cards is dealt from a regular pack of fifty two cards.a) What is the number of possible hands?552 Hands C2598960b) What is the probability of getting three of a kind?113 Hands Ckind" a ofthree"hasnumber which choose34C 248Ccardsthoseof threechooserestthefromcardstworemainingchoose58656 259896058656kind a of three P291594 (=3.2%)A four person team is to be chosen at random from nine women and seven men.2004 Extension 1 HSC Q2e)(i) In how many ways can this team be chosen?A four person team is to be chosen at random from nine women and seven men.2004 Extension 1 HSC Q2e)(i) In how many ways can this team be chosen?416 Teams CA four person team is to be chosen at random from nine women and seven men.2004 Extension 1 HSC Q2e)(i) In how many ways can this team be chosen?416 Teams C With no restrictions, choose 4 peoplefrom 16, gender does not matter A four person team is to be chosen at random from nine women and seven men.2004 Extension 1 HSC Q2e)(i) In how many ways can this team be chosen?416 Teams C With no restrictions, choose 4 peoplefrom 16, gender does not matter 1820A four person team is to be chosen at random from nine women and seven men.2004 Extension 1 HSC Q2e)(i) In how many ways can this team be chosen?(ii) What is the probability that the team will consist of four women?416 Teams C With no restrictions, choose 4 peoplefrom 16, gender does not matter 1820A four person team is to be chosen at random from nine women and seven men.2004 Extension 1 HSC Q2e)(i) In how many ways can this team be chosen?(ii) What is the probability that the team will consist of four women?416 Teams C With no restrictions, choose 4 peoplefrom 16, gender does not matter 182049 Teams CA four person team is to be chosen at random from nine women and seven men.2004 Extension 1 HSC Q2e)(i) In how many ways can this team be chosen?(ii) What is the probability that the team will consist of four women?416 Teams C With no restrictions, choose 4 peoplefrom 16, gender does not matter 182049 Teams C By restricting it to only women, there is only 9 people to choose fromA four person team is to be chosen at random from nine women and seven men.2004 Extension 1 HSC Q2e)(i) In how many ways can this team be chosen?(ii) What is the probability that the team will consist of four women?416 Teams C With no restrictions, choose 4 peoplefrom 16, gender does not matter 182049 Teams C126By restricting it to only women, there is only 9 people to choose fromA four person team is to be chosen at random from nine women and seven men.2004 Extension 1 HSC Q2e)(i) In how many ways can this team be chosen?(ii) What is the probability that the team will consist of four women?416 Teams C With no restrictions, choose 4 peoplefrom 16, gender does not matter 182049 Teams C126By restricting it to only women, there is only 9 people to choose from 1820126m women tea4 PA four person team is to be chosen at random from nine women and seven men.2004 Extension 1 HSC Q2e)(i) In how many ways can this team be chosen?(ii) What is the probability that the team will consist of four women?416 Teams C With no restrictions, choose 4 peoplefrom 16, gender does not matter 182049 Teams C126By restricting it to only women, there is only 9 people to choose from 1820126m women tea4 P1309A four person team is to be chosen at random from nine women and seven men.2004 Extension 1 HSC Q2e)(i) In how many ways can this team be chosen?(ii) What is the probability that the team will consist of four women?416 Teams C With no restrictions, choose 4 peoplefrom 16, gender does not matter 182049 Teams C126By restricting it to only women, there is only 9 people to choose from 1820126m women tea4 P1309Exercise 10G; odd(not 19, 27)Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Slide Number 37Slide Number 38Slide Number 39Slide Number 40Slide Number 41Slide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Slide Number 47Slide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54Slide 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