Question

How many ways can 15 people be chosen from a group of 22

Answer 1

Answer:

$170544\text{ ways}$

Step-by-step explanation:

If we don't care about the order (like if we pick Bob then Joe vs Joe then Bob), then a formula is $\frac{n!}k!{(n-k)!}$ where we are picking k items from a list of n items

In our case, n=22 and k=15

Therefore, there are $\frac{22!}{15!(22-15)!}=$

$\frac{22*21*20*19*18*17*16}{(7)!}=$

$\frac{22*21*20*19*18*17*16}{7*6*5*4*3*2*1}=$

$\frac{2*11*7*3*5*4*19*6*3*17*16}{7*6*5*4*3*2*1}=$

$11*19*3*17*16=$

$170544\text{ ways}$