Question

video lesson 5.5 example 2 - using a permutations formula

1. eight people serve on a committee. in how many different ways can a chairperson, a recorder, and a treasurer be chosen from the committee members?

Explanation:

Step1: Identify the problem type

This is a permutation problem since the order of selection (chairperson, recorder, treasurer) matters. The permutation formula is \( P(n, r)=\frac{n!}{(n - r)!} \), where \( n = 8 \) (total people) and \( r = 3 \) (positions to fill).

Step2: Apply the permutation formula

Substitute \( n = 8 \) and \( r = 3 \) into the formula: \( P(8, 3)=\frac{8!}{(8 - 3)!}=\frac{8!}{5!} \).

Step3: Simplify the factorials

Since \( 8! = 8\times7\times6\times5! \), we can cancel out \( 5! \) from the numerator and denominator: \( \frac{8\times7\times6\times5!}{5!}=8\times7\times6 \).

Step4: Calculate the result

\( 8\times7\times6 = 336 \).

Answer:

336