From a group of 8 men and 7 women, 5 persons are to be selected to form a committee so that at least 4 men are there on the committee. In how many ways can it be done?


Answer:

546

Step by Step Explanation:
  1. We are required to select a 5-member committe from a group of 8 men and 7 women with at least 4 men. This can be done in 2 different ways:-
    1. 4 men and 1 woman
    2. 5 men
  2. Number of ways of selecting 4 men and 1 woman =8C4×7C1 =8!4!(84)!×7!1!(71)!=490
    Number of ways of selecting 5 men =8C5 =8!5!(85)!=56
  3. Now, required number of ways of selecting a 5-member committee =490+56=546
    Hence, there are 546 ways of selecting a 5-member committee with at least 4 men.

You can reuse this answer
Creative Commons License