Solve the problem.
-Given a group of students: $\mathrm { G } = \{$ Allen, Brenda, Chad, Dorothy, Eric, Frances, Gale $\}$, count the number of different ways of choosing 4 people for a committee. Assume no one can hold more than one office and that each person is to hold a different position on the committee.
A) 5040
B) 840
C) 35
D) 2401

Question

Quizplus · Accepted Answer

The number of ways to choose 4 people out of 7 for different positions is calculated using permutations since the order matters. The formula for permutations is $P(n, k) = \frac{n!}{(n-k)!}$. Here, $n = 7$ and $k = 4$, so $P(7, 4) = \frac{7!}{(7-4)!} = \frac{7!}{3!} = \frac{7 \times 6 \times 5 \times 4}{1} = 840$.

Solve the Problem G={\mathrm { G } = \{G={ Allen, Brenda, Chad, Dorothy, Eric, Frances, Gale

Solve the Problem $\mathrm { G } = \{$ Allen, Brenda, Chad, Dorothy, Eric, Frances, Gale