Multiple choice

Three men are to be selected from among A, B, C, D, and E. If A is selected, D cannot be selected. In how many ways can the three men be selected?

  1. 4

  2. 5

  3. 7

  4. 10

  5. 12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total ways to choose 3 from 5 is 5C3 = 10. If A is selected, we need to choose 2 more from {B, C, E} (since D cannot be selected). This is 3C2 = 3 ways. If A is not selected, we choose 3 from {B, C, D, E}, which is 4C3 = 4 ways. Total = 3 + 4 = 7.

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