Question

A company is selecting 6 people to be on a committee. There are 29 employees eligible to be on the committee. What is the total number of ways the committee may be formed if the employees are selected at random and each employee will have a different position on the committee? (One person will be president, another vice president, ...)

Answer 1

Answer: 342014400

Step-by-step explanation:

Given : A company is selecting 6 people to be on a committee.

Total employees eligible to be on the committee=29

Since each employee will have a different position on the committee, thus order matters here , so we use Permutations.

Number of permutation of n thing taking m things at a time is given by :-

$^nP_m=\dfrac{n!}{(n-m)!}$

Then, the number of permutation of 29 employees taking 6 at a time will be :-

$^{29}P_6=\dfrac{29!}{(29-6)!}\\\\=\dfrac{29\times28\times27\times26\times25\times24\times23!}{23!}\\\\=342014400$

Hence, the total number of ways the committee may be formed = 342014400