A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen?
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givemeanid
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The committe can be
1. 3 officers 2 civilians OR
2. 2 officers 3 civilians
Total number of ways to choose 1 = 5C3 * 9C2 = 10 * 36 = 360
Total number of ways to choose 2 = 5C2 * 9C3 = 10 * 84 = 840
So, altogether, total number of ways = 360+840 = 1200
1. 3 officers 2 civilians OR
2. 2 officers 3 civilians
Total number of ways to choose 1 = 5C3 * 9C2 = 10 * 36 = 360
Total number of ways to choose 2 = 5C2 * 9C3 = 10 * 84 = 840
So, altogether, total number of ways = 360+840 = 1200
So It Goes
