Multiple choice

In how many ways can 3 persons out of 4 couples be selected, such that there is no couple among them?

  1. 24

  2. 28

  3. 32

  4. 36

  5. 56
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total ways to choose 3 people from 8 is 8C3 = 56. To have no couple, we must choose 3 couples out of 4 (4C3 = 4 ways) and then choose 1 person from each of those 3 couples (2^3 = 8 ways). Total ways = 4 * 8 = 32.

AI explanation

First, select 3 different couples out of the 4 couples, which can be done in 4C3 ways. From each of these 3 chosen couples, select exactly 1 person, which can be done in 2C1 ways per couple. The total number of ways is 4C3 times 2C1 times 2C1 times 2C1, which equals 4 times 2 times 2 times 2, giving 32.

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