Question 967134
A majority means more than 50%


Since 1/3 = 33% roughly and 2/3 = 67% roughly, this means that if we must have a "majority of men", then the committee must have 2 or more men.


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If we have 2 men, then...


12 C 2 = 66 ways to pick 2 men (from a pool of 12)
10 C 1 = 10 ways to pick 1 woman (from a pool of 10)


So 66*10 = 660 ways to pick 2 men & 1 woman


note: I'm using the <a href="http://www.mathwords.com/c/combination_formula.htm">Combination Formula</a> when I refer to something like 12 C 2 (basic template: n C r)


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If we have 3 men, then...


12 C 3 = 220 ways to pick 2 men (from a pool of 12)
10 C 0 = 1 way to pick 0 woman (from a pool of 10)


So 220*1 = 220 ways to pick 3 men & 0 women


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Add up the subtotals: 660+220 = 880


Final Answer: There are 880 ways to pick a committee where the majority must be men.