WebMar 13, 2015 · 8 choose 3 is the number of ways of choosing 3 different runners from 8 but you haven't accounted for the fact that once you've picked three, they can come in a number of different orders, specifically the number of permuations of 3 elements (i.e. 3!=6). So the final answer is. ( 8 3) × 3! = 56 × 6 = 336. Share. WebIn how many ways may these same people line up if two of the people refuse to stand next to each other? 8. In how many ways may 8 people form a circle for a folk dance? ... If eight …

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WebJun 15, 2016 · For the first position there will be 9 people to choose from. Once that person is chosen, there are 8 to choose from for the second person and so on, until for the last person there will only be 1 person left for the last position. This is called 9 factorial (9!) and means 9x8x7x6x5x4x3x2x1. Answer link WebJun 20, 2024 · (ii) you can choose between 3 males for the beginning of the line, between 2 for the end of the line, and then you sort 6 people in the remaining 6 places. $3 \times 2 \times 6! = 4320$ (iii) you subcommittee has to contain at least one male, so we can calculate every possible committee and then subtract the ones with only women. incompetent\u0027s b

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WebTheorem 3 - Permutations of Different Kinds of Objects . The number of different permutations of n objects of which n 1 are of one kind, n 2 are of a second kind, ... n k are of a k-th kind is `(n!)/(n_1!xxn_2!xxn_3!xx...xx n_k!` Example 5 . In how many ways can the six letters of the word "mammal" be arranged in a row? Answer WebJul 17, 2024 · Suppose we have three people named A, B, and C. We have already determined that they can be seated in a straight line in 3! or 6 ways. Our next problem is to see how many ways these people can be seated in a circle. We draw a diagram. It happens that there are only two ways we can seat three people in a circle, relative to each other’s … WebIf no one's sat down, there's five different possibilities for seat number one. And then for each of those possibilities, there's four people who could sit in seat number two. And then … incompetent\u0027s b2