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

Answer:

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

Step-by-step 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 = $\frac{n!}{x! (n-x)!}$

n = the number of items.

x = how many items are taken at a time.

As given, n = 16 , x = 3

⇒¹⁶C₃ = $\frac{16!}{3! (16-3)!} = \frac{16!}{3! (13)!} = \frac{16.15.14.13!}{3! (13)!} = \frac{16.15.14}{3!} = \frac{16.15.14}{3.2.1} = \frac{3360}{6} = 560$

∴ we get

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