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.