Answer:
[tex]170544\text{ ways}[/tex]
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 [tex]\frac{n!}k!{(n-k)!}[/tex] where we are picking k items from a list of n items
In our case, n=22 and k=15
Therefore, there are [tex]\frac{22!}{15!(22-15)!}=[/tex]
[tex]\frac{22*21*20*19*18*17*16}{(7)!}=[/tex]
[tex]\frac{22*21*20*19*18*17*16}{7*6*5*4*3*2*1}=[/tex]
[tex]\frac{2*11*7*3*5*4*19*6*3*17*16}{7*6*5*4*3*2*1}=[/tex]
[tex]11*19*3*17*16=[/tex]
[tex]170544\text{ ways}[/tex]
