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How many 3 person groups can be formed in a club of 8 people How do you Solve This I know that the answer is 56 but do not know how to reach the answer.?
Solastsunday152
I know 8x3=24 then 24 plus 32 i got 32 coz I minus 56 and 24 :) but i am not sure for this
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When s units is pulled from a population of N, you could use the formula:
(N)'s' / s! = N*(N-1)*(N-2)*(N-3)...(N-s+1) / s! = N! / s!*(N-s)! Which in your case translates into: 8*7*6 / 3*2*1 = 336 / 56 = 56 If you want to learn more, check out a statistics textbook. Chibster
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This situation is a combination, since from a group of 9 people, 4 are chosen and the order in which they are chosen is not important. So we have9C4 = (9 x 8 x 7 x 6 )/(4 x 3 x 2 x 1) = 126.The following explanation will tell you why we got this result.The first person can be any one of 9.The second person can be any one of the remaining 8.The third person can be any one of the remaining 7.The fourth person can be any one of the remaining 6.The number of ways to make this choice of 4 people is (9 x 8 x 7 x 6) = 3,024.This is a permutation, and that's what the question asked for when it asked ... "How many ways ... ".But not all of the groups chosen in these 3,024 ways are different groups. In fact, each differentgroup will show up 24 times, because 4 people can be arranged (4 x 3 x 2 x 1) = 24 ways.So the number of combinations, i.e. different groups of 4 people, is (3,024 / 24) = 126.
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