Question

(a) how many ways can a 2-person subcommittee be selected from a committee of 9 people? (b) how many ways can a president and vice-president be chosen from a committee of 9 people? (a) the number of ways to select a 2-person subcommittee is \\(\square\\). (b) the number of ways to choose a president and vice-president is \\(\square\\).

Explanation:

Step1: Use combination formula for (A)

Combination formula: $C(n,k)=\frac{n!}{k!(n-k)!}$. Here $n=9,k=2$.
$C(9,2)=\frac{9!}{2!7!}=\frac{9×8}{2×1}=36$.

Step2: Use permutation formula for (B)

Permutation formula: $P(n,k)=\frac{n!}{(n-k)!}$. Here $n=9,k=2$.
$P(9,2)=\frac{9!}{7!}=9×8=72$.

Answer:

(A) 36
(B) 72