Question

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

Answer 1

The inquiries can be directed to the agents in 369,600 ways.

Step-by-step explanation:

This question is about permutations, which is a topic in Combinatorics. In this case, we want to find the number of ways to assign 12 inquiries to 4 real estate agents, with each agent handling 3 inquiries. We can solve this problem using a combination of multiplication and factorials.

First, we need to select 3 inquiries for the first agent. We can choose 3 inquiries from the 12 total inquiries in 12C3 ways. This can be calculated as 12! / (3! * (12-3)!).

After the first agent has 3 inquiries, there will be 9 inquiries left. We can then choose 3 inquiries for the second agent from the remaining 9 inquiries in 9C3 ways.

Similarly, we can choose 3 inquiries for the third agent from the remaining 6 inquiries in 6C3 ways.

Finally, the fourth agent will automatically receive the remaining 3 inquiries.

Therefore, the total number of ways to direct the inquiries is 12C3 * 9C3 * 6C3 = 220 * 84 * 20 = 369,600 ways.