Correct Answer - Option 2 : 63
Formula used:
If we have a group of 'n' objects out of which we make a selection taking 'r' object at a time, then the number of such selections is given by the combination formula
nCr = n!/(r!(n – r!))
Calculation:
Number of groups can be formed by 5 men and 2 women out of 7 men and 3 women
⇒ 7C5 × 3C2
⇒ 7!/(5! × (7 – 5)!) × 3!/(2! × (3 – 2)!)
⇒ 7!/(5! × 2!) × 3!/(2! × 1!)
⇒ (7 × 6 × 5!)/(5! × 2) × (3 × 2!)/(2!)
⇒ (7 × 3) × (3)
⇒ 63
∴ The number of ways to arrange men and women is 63
