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DIRECTION for the question: Solve the following question and mark the best possible option.
From a group of 7 men and 6 women, 5 persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
We have to select at least $$3$$ men.
So we can either select $$3$$, $$4$$ or $$5$$ men
Case 1: $$3$$ Men, $$2$$ Women
Total number of ways = $$^7C_3 \times ^6C_2 = 35 \times 15 = 525$$
Case 2: $$4$$ Men, $$1$$ Woman
Total number of ways = $$^7C_4 \times ^6C_1 = 35 \times 6 = 210$$
Case 3: $$5$$ Men, $$0$$ Woman
Total number of ways = $$^7C_5 \times ^6C_0 = 21 \times 1 = 21$$
Total number of ways = $$525 + 210 + 21 = 756$$
Hence, option D is the correct choice.
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