Question

(A) How many ways can a 2-person subcommittee be selected from a committee of 8 people?

Answer 1

To solve this problem, we have to use the combination formula

$C^r_n=\frac{n!}{r!(n-r)!}$

Where r represents the number of people for the subcommittee (2), and n represents the total committee (8). Replacing this information, we have

$C^2_8=\frac{8!}{2!(8-2)!}=\frac{8!}{2!(6)!}$

Remember that factorials are solved by multiplying the number in a reversal way, as follows

$C^2_8=\frac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(2\cdot1)(6\cdot5\cdot4\cdot3\cdot2\cdot1)}=\frac{40,320}{2(720)}=\frac{40,320}{1,440}=28$

Therefore, there are 28 ways to form a 2-person subcommittee from a committee of 8.