In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

Solution:

We know that the number of ways of selecting r different things from n different things is a combination and is calculated using the formula ⁿCᵣ = n! / [r!(n−r)!].

Thus, the number of ways of selecting 3 boys from 5 boys = ⁵C₃ and

the number of ways of selecting 3 girls from 4 girls = ⁴C₃

By fundamental principle of counting,

The required number of ways = ⁵C₃ × ⁴C₃

= (5!) / [3! (5-3)!] × (4!) / [3! (4-3)!] (Using nCr formula)

= 10 × 4

= 40

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.4 Question 4

In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?

Summary:

The number of ways in which a team of 3 boys and 3 girls can be selected from 5 boys and 4 girls is 40