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Seventy-five people buy a raffle ticket for a cake drawing with four cakes. If four tickets are to be drawn, how many ways are there to award the cakes if the four cakes are a. identical? b. different?

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Answer:

a. 1,215,454 ways

b. 29,170,800 ways

Step-by-step explanation:

a. If the four cakes are identical, order does not matter, and the total number of ways to award the cakes is given by a combination, C(75,4):

[tex]C(75,4) = \frac{75!}{(75-4)!4!}\\C(75,4) = \frac{75*74*73*72}{4*3*2*1}\\C(75,4) = 1,215,454[/tex]

b. If the four cakes are different, order does matter, and the total number of ways to award the cakes is given by a permutation, P(75,4):

[tex]P(75,4) = \frac{75!}{(75-4)!}\\C(75,4) = 75*74*73*72\\C(75,4) = 29,170,800[/tex]

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