4. Fifteen students competed in an ice cream eating contest. The first place win

Question

4. Fifteen students competed in an ice cream eating contest. The first place winner will receive $100, the second place winner will receive $50, and the third place winner will receive $25. In how many ways can the three winners be drawn?

5. Before the contest, each contestant shakes hands with the other contestants, wishing them good luck." How many handshakes took place?

6. In the ice cream shop they have 20 tubs of ice cream and seven freezers. How many ways are there to put 20 tubs of ice cream in seven freezers if each freezer can easily

hold twenty tubs and if it is not necessary that each freezer has a tub of ice cream in it?

7. What if we change the rules to the question above and insist that each freezer must hold at least one tub of ice cream?

Explanation / Answer

4.

Order matters, so we use permutations.

Hence, there are

15P3 = 15!/(15-3)! = 2730 ways [ANSWER]

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5.

As handshakes take 2 persons, then

15C2 = 15!/(2!13!) = 105 handshakes [ANSWER]

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