Question

For each question, show the formulas or calculations to support your answer, in addition to the final answer. Large numbers can be left in factorial form in the answers, e.g., (100! / 3!)

1. There are 28 unique dominoes in a set. How many different sets of seven dominoes could a player be dealt?

2. How many different five-letter words can be created from the characters AXBDEFGLK, if each character can be used multiple times?

3. A candy maker makes 12 different types of candy. How many different bags of 10 pieces can be created?

Answer 1

(1)

7 dominoes can be chosen from 28 dominoes in C(28, 7) ways

Number of ways = C(28, 7) = 28! / (28 - 7)! 7!) = 28! / (21! 7!) = 1184040

(2)

There are 9 letters given and each letter can be used multiple times

Number of 5-letter words = 9 * 9 * 9 * 9 * 9 = 59049

(3)

10 candies can be chosen from 12 candies in C(12, 10) ways

Number of bags = C(12, 10) = 12! / (12 - 10)! 10!) = 12! / (2! 10!) = 66

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