Question

Customers at Beans Coffee Shop have entered their name in a drawing for one of 4 gift cards. The gift cards each have a value of $10. If 79 customers enter the drawing, what is the total number of ways Beans Coffee Shop could choose the winners?

Answer 1

36,060,024 ways

Explanation:

To choose the winner in this case, the order is very important because it determines who is chosen first out of the seventy-nine customers whose names were entered for the draw.

The above supports the reason Permutation will be used instead of Combination.

The total number of ways is given by:

⁷⁹P₄ = 79!/(79-4)!

= 79!/75!

= [79 x 78 x 77 x 76 x75!]/75!

= 79 x 78 x 77 x 76

= 36,060,024 ways

This implies that there are 36,060,024 ways the Bean Coffee Shop could choose the winners.