Question

In how many ways can a man and a woman be chosen out of 10 men and 8 women?
1. 18
2. 80
3. 40
4. 10

Answer 1

Correct Answer - Option 2 : 80

Given:

Number of men = 10

Number of women = 8

Concept used:

Number of ways in which one man and woman can be chosen from a group of ‘n’ men and m woman = ⁿC₁ × ^mC₁

ⁿC_r = n!/[r! × (n – r)!]

Calculation:

Number of ways in which one man and woman can be chosen from a group of 10 men and 8 women = ¹⁰C₁ × ⁸C₁ = 10 × 8

Number of ways in which one man and woman can be chosen from a group of 10 men and 8 women = 80

∴ The number of ways in which one man and woman can be chosen from a group of 10 men and 8 women is 80