Question

There are 50 runners in a race. How many ways can the runners finish first, second, and third?

Answer 1

Number of ways can the runners finish first, second, and third is 1,17,600 .

Explanation:

Permutation is the act of arranging the members of a set into a sequence or order, or, if the set is already ordered, rearranging (reordering) its elements—a process called permuting. For example, written as tuples, there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). Formula of Permutation is :
`P(n,r) = (n!)/((n-r)!)` where n is the number of things to choose from, and we choose r of them, no repetitions, order matters. Here , n = 50 , r= 3

⇒
`P(n,r) = (n!)/((n-r)!)`

⇒
`P(50,3) = (50!)/((50-3)!) = (50(49)(48)47!)/(47!)`

⇒
`P(50,3) = 50(49)(48)`

⇒
`P(50,3) = 1,17,600`

∴ Number of ways can the runners finish first, second, and third is 1,17,600 .