Question

a club has 6 members running for president, vice president, and secretary. how many different ways can these three positions be filled if each person can hold only one position?
_{6}p_{3} = ?

Explanation:

Step1: Recall permutation formula

Permutation formula: $P(n,k)=\frac{n!}{(n-k)!}$

Step2: Substitute n=6, k=3

$P(6,3)=\frac{6!}{(6-3)!}=\frac{6×5×4×3!}{3!}$

Step3: Simplify the expression

Cancel $3!$: $6×5×4=120$

Answer:

120