Multiple choice

In how many ways can we select 6 men and 5 women from 10 men and 12 women?

  1. 22C11

  2. 12C6 × 10C5

  3. 10C6 × 12C5

  4. 106 × 125

  5. 126 × 105
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Selecting 6 men from 10 is 10C6. Selecting 5 women from 12 is 12C5. Total ways = 10C6 * 12C5.

AI explanation

To find the total number of ways to select the committee, use the basic principle of combination for independent choices. The 6 men must be chosen from 10 men, which can be done in 10C6 ways. The 5 women must be chosen from 12 women, which can be done in 12C5 ways. Because these selections happen independently, multiply the combinations to get the total ways: 10C6 times 12C5.

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