Question

Suppose that 21 people are competing in an Olympic event, where first place earns Gold, second place earns Silver, and third place earns Bronze. How many different possible outcomes are there for this Olympic event

Answer 1

Explanation:

This is a combination problem. Combination has to do with selection

Total people competing in the event = 21people

Prizes to be won = 3(Gold, silver and bronze)

Using the formula

nCr = n!/(n-r)!r!

21C3 = 21!/(21-3)!3!

21C3 = 21!/18!3!

21C3 = 21×20×19×18!/18!3!

21C3 = 21×20×19/3!

21C3 = 21×20×19/6

21C3 = 1330

Hence 1330 possible outcome are there for the event.