Question

C & J Realty has received 12 inquiries from prospective home buyers. In how many ways can the inquiries be directed to any three of the firm's real estate agents if each agent handles four inquiries? ——- ways

Answer 1

Answer:

The number of ways the inquiries directed = 34,650

Step-by-step explanation:

Here we have to use the permutation.

If number of different permutations of "n" objects where there are $n_1$ repeated items, $n_2$ ....$n_k$  repeated items, then the number of ways = $\frac{n!}{n_1! n_2!...n_k!}$

Given:

Then number calls received = 12. So n = 12

The number of real estate agents = 3 and each agent handles 4 inquiries.

The number of ways the inquiries directed = $\frac{12!}{4!.4!.4!}$

= $\frac{479,001,600}{24.24.24}$

=  $\frac{479,001,600}{13824}$

= 34,650 ways

So, the number of ways the inquiries directed = 34,650