Question

Eight people sit in chairs in a room.

In how many ways can four of these people be chosen to stand up?
__ways

Answer 1

70

Explanation:

You want to know the number of ways 4 people can be chosen from 8.

8 Choose 4

There are 8 ways to choose the first person, 7 ways to choose the second, 6 ways to choose the third, and 5 ways to choose the fourth. That gives a total of 8·7·6·5 = 1680 possible permutations.

However, we're only interested in the people standing, not the order in which they got to be standing. Hence, we can divide this number by the number of possible orders in which the people could stand: 4! = 24.

1680/24 = 70

There are 70 ways 4 of 8 people can be chosen to stand up.

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Additional comment

The function that computes "n choose k" (nCk) is the same function that computes coefficients of a binomial expansion.

nCk = n!/(k!(n-k)!)