What is the probability of a social service has 15 new clients and wants to assign 5 clients to each of three specific case workers. in how many ways can this be done?

To assign 5 clients to each of three specific case workers from a total of 15 new clients, we can use the multinomial coefficient. The number of ways to do this is given by the formula:

[ \frac{15!}{5!5!5!} ]

Calculating this yields:

[ \frac{15!}{5!^3} = \frac{1,307,674,368,000}{120 \times 120 \times 120} = 3,603,600 ]

Thus, there are 3,603,600 ways to assign the clients to the case workers.