Question

Mary has 5 boxes of candy that she wants to hand out as random prizes at her meeting. There are 20 people at her meeting. How many different ways can Mary choose 5 different people to award the candy?

Answer 1

Answer:

It can be done 15,504 number of ways.

Step-by-step explanation:

This is a combination problem since we are selecting 5 different people out of a pool of 20people to award the candies. Combination has to do with selection.

Generally, if r people are selected from a pool of n people, this can be done in nCr number of ways.

$nCr = \frac{n!}{(n-r)!r!}$

To select 5different people out of 20 people, this can be done in 20C5 ways as shown;

$20C5 = \frac{20!}{(20-5)!5!}\\= \frac{20!}{15!5!}\\ = \frac{20*19*18*17*16*15!}{15!*5*4*3*2*1}\\= \frac{19*18*17*16}{6} \\= 19*3*17*16\\= 15,504ways$

It can be done 15,504 number of ways.