Question

From a group of 7 men and 6 women , a committee of 5 person with more males than females is to be formed . In how many ways can this be done ?
1. 564
2. 645
3. 735
4. 756

Answer 1

Correct Answer - Option 4 : 756

Formula Used:

Number of ways of selection of  r items out of  n items: ⁿC_r   = n!/((n-r)! × r!)

Concept:

Probable combinations of selection could be as follows:

Cases	Required number of Males	Required number of Females
I	3	2
II	4	1
III	5	0

 

Calculation:

Number of ways: ⁷C₃  × ⁶C₂ + ⁷C₄ × ⁶C₁ + ⁷C₅ × ⁶C₀

⇒ 35× 15 + 35× 6 + 21× 1

⇒ 756

Number of ways in which the following activities can be done = 756