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Probability, Statistics and Queueing

Three committee members are chosen from 8 people. If the members have no distinct roles, which of the following is the number of possible choices?

  1. A56
  2. B336
  3. C512
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Answer: A. 56

Since the members have no distinct roles, the order of selection does not matter, so the number of combinations 8C3 is needed. 8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1) = 56. It can also be seen as the number of permutations 8P3 = 336, which distinguishes the order, divided by 3! = 6, the number of ways to order the same three people.

  • A. Correct. 8C3 = 336 ÷ 6 = 56.
  • B. This is the number of permutations 8P3 = 8 × 7 × 6, which distinguishes the order of selection. Because there are no distinct roles, it must be divided by the 6 ways of ordering the same three people.
  • C. This is 8³ = 512, which allows the same person to be chosen any number of times and also distinguishes the order.
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