In how many ways can a group of 5 men and 2 women be made out of a tot

1.	In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?1. 452. 633. 904. 126
Answer» 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 ⁿC_r = 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

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?1. 452. 633. 904. 126

Answer» 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

ⁿC_r = 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

Discussion

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