Question

A group of 7 members having a majority of boys is to be formed out of 6 boys and 4 girls. The number of ways the group can be formed is
1. 80
2. 100
3. 90
4. 110

Answer 1

Correct Answer - Option 2 : 100

Given:

A Group of 7 members with the majority of boys can be formed in the following ways

Formula used:

ⁿC_r = (n!)/[(n - r)! r!]

Calculations:

Possible combinations According to the question

Case 1: 4 boys and 3 girls

Case 2: 5 boys and 2 girls

Case 3: 6 boys and 1 girl

Case 1 combinations:

Select 4 boys out of 6 = (⁶C₄ ways) 

Select 3 girls out of 4 = (⁴C₃ ways)

Total ways = 6C4 × 4C3 = 60 ways

Case 2 combinations:

Select 5 boys out of 6 = (6C5 ways)

Select 2 girls out of 4 =  (4C2 ways)

Total ways = 6C5 × 4C2 = 36 ways

Case 3 combination s:

Select 6 boys out of 6 (1 way)

Select 1 girl out of 4 = (4C1 ways)

Total ways = 1 × 4C1 = 4 ways

Total possible combinations = 60 + 36 + 4 = 100 ways

∴ The total possible combinations are 100