Question

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

Answer 1

`170544\text{ ways}`

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
`(22!)/(15!(22-15)!)=`

`(22*21*20*19*18*17*16)/((7)!)=`

`(22*21*20*19*18*17*16)/(7*6*5*4*3*2*1)=`

`(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}`