Number of ways can the runners finish first, second, and third is 1,17,600 .
<u>Step-by-step explanation:</u>
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 :
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) = \frac{n!}{(n-r)!}](https://tex.z-dn.net/?f=P%28n%2Cr%29%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
⇒ ![P(50,3) = \frac{50!}{(50-3)!} = \frac{50(49)(48)47!}{47!}](https://tex.z-dn.net/?f=P%2850%2C3%29%20%3D%20%5Cfrac%7B50%21%7D%7B%2850-3%29%21%7D%20%3D%20%5Cfrac%7B50%2849%29%2848%2947%21%7D%7B47%21%7D)
⇒ ![P(50,3) = 50(49)(48)](https://tex.z-dn.net/?f=P%2850%2C3%29%20%3D%2050%2849%29%2848%29)
⇒ ![P(50,3) = 1,17,600](https://tex.z-dn.net/?f=P%2850%2C3%29%20%3D%201%2C17%2C600)
∴ Number of ways can the runners finish first, second, and third is 1,17,600 .