Question

Seventy-five (75) customers at Crummy Burger today were entered in a drawing. Three names will be drawn, and each will win a prize. Determine the number of ways that the prizes can be distributed if first prize is a $25 gift card, second prize is a free Crummy Combo Meal, and third prize is a free Jumbo Crummy Burger.

Answer 1

405150

Explanation:

3 people are to be selected from 75 people. This could be done using the combination function,
`\binom{75}{3}`. 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

`\binom{75}{3}*3! = 405150`

In fact, this is the permutation function given by

`{}^(75)P_3 = (75!)/((75-3)! = 405150)`