Answer:
405150
Step-by-step explanation:
3 people are to be selected from 75 people. This could be done using the combination function, [tex]\binom{75}{3}[/tex]. But thus function only gives the number of ways of choosing any 3 out of the 75 customers. For any single selection of any 3 customers, there are 3! ways of sharing the three prizes among them. Hence the total number of ways of sharing the prizes is
[tex]\binom{75}{3}\times3! = 405150[/tex]
In fact, this is the permutation function given by
[tex]{}^{75}P_3 = \dfrac{75!}{(75-3)! = 405150}[/tex]
