Combinatorics Intermediate Challenges-IV
A committee of 4 senior members and 2 junior members must be selected from 6 senior members and 5 junior members. One of the senior members is a cousin of one of the junior members. The organizers decide that at most one of these cousins can be included in the committee. In how many ways can the committee be selected?
This problem is part of this set .
The answer is 110.
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1 solution
Without restrictions, there are ( 4 6 ) ( 2 5 ) = 1 5 ∗ 1 0 = 1 5 0 possible committees.
From this total, we need to subtract those committees that include both cousins. There are ( 3 5 ) ( 1 4 ) = 1 0 ∗ 4 = 4 0 of these.
Thus the number of committees that include at most one of the cousins is 1 5 0 − 4 0 = 1 1 0 .