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?

Question

Mathematics

Obrien

7 September, 04:16

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?

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Answers (1)

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Zaniyah Novak · Answer 1

36,060,024 ways

Step-by-step 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.