Question

A class has 6 boys and 7 girls,, out of them they have to select group of 6 students for performing a mime,
so that the selected group should have at least 4 girls.​

Answer 1

Given: Number of boys = 6

Number of girls = 7

Number of students in the group = 6

Number of girls mandatory to be in the group = 4

To find: Number of ways the group can be formed

Solution:

Number of ways in which the group can be formed where it has 4 girls =

⁷C₄ × ⁶C₂ = 35 × 15 = 525

Number of ways in which the group can be formed where it has 5 girls =

⁷C₅ × ⁶C₁ = 21 × 6 = 126

Number of ways in which the group can be formed where it has 6 girls =

⁷C₆ × ⁶C₀ = 7 × 1 = 7

Hence, total number of ways the group can be formed in which there are at least 4 girls = 525 + 126 + 7 = 658

Answer: 658