Multiple choice

From a group of six persons A, B, C, D, E and F, a committee of four is to be formed. In how many ways can it be done if E is also selected whenever B is selected?

  1. 5

  2. 6

  3. 0

  4. 11
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total ways to choose 4 from 6 is 6C4 = 15. Cases where B is selected: B must be in, E must be in. We need 2 more from the remaining 4 (A, C, D, F), which is 4C2 = 6. Cases where B is NOT selected: We choose 4 from the remaining 5 (A, C, D, E, F), which is 5C4 = 5. Total valid ways = 6 + 5 = 11.

AI explanation

We form a committee of four from six people, so we calculate the total unrestricted combinations using the combination formula: 6 C 4 equals 15. If B is selected without E, we must fill the remaining 3 spots from the 4 people who are neither B nor E, which gives 4 C 3 equals 4 ways. We subtract these 4 invalid committees from the total 15 to get 11 valid ways.

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