Question

Sixteen players participated in a tennis tournament. Three players will be awarded for first, second, and third prize. In how many different ways can first, second and third prizes be awarded?

Answer 1

Total number of ways in which first, second and third prizes will be awarded = 560

Explanation:

As given,

There are 16 players participated in a tennis tournament.

and 3 players will be awarded for first, second, and third prize.

As we know,

ⁿCₓ =
`(n!)/(x! (n-x)!)`

n = the number of items.

x = how many items are taken at a time.

As given, n = 16 , x = 3

⇒¹⁶C₃ =
`(16!)/(3! (16-3)!) = (16!)/(3! (13)!) = (16.15.14.13!)/(3! (13)!) = (16.15.14)/(3!) = (16.15.14)/(3.2.1) = (3360)/(6) = 560`

∴ we get

Total number of ways in which first, second and third prizes will be awarded = 560