Question

How many ways can a committee of 4 be selected from a club with 10 members?

Answer 1

If all committee members have identical jobs, then there are
C(10,4)=10!/(4!(10-4)!)=10!/(4!6!)=10*9*8*7/(1*2*3*4)=210
ways to select 4 committee members from a club of 10 members.

Answer 2

You have to select 4 members for a committee. These members are with the same powers, so you should use combinations

`C_n^k=(n!)/(k!(n-k)!).`

In your case, n=10, k=4, then

`C_(10)^4=(10!)/(4!(10-4)!)=(10!)/(4!\cdot 6!)=(6!\cdot 7\cdot 8\cdot 9\cdot 10)/(6!\cdot 2\cdot 3\cdot 4)=7\cdot 3\cdot 10=210.`

Answer: 210 ways to select a committee of 4 members from 10 members.