Question

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

Answer 1

Given that,

We need to select a team consisting of 3 boys and 3 girls out of 5 boys and 4 girls. 

Let us assume the no. of ways of selection be N. 

⇒ N = (Selecting 3 boys out of 5 boys) × (selecting 3 girls out of 4 girls) 

⇒ N = (⁵C₃) × (⁴C₃) 

We know that,

ⁿC_r = \(\frac{n!}{(n-r)!r!}\)

And also,

n! = (n)(n – 1)......2.1

⇒ N = (10) × (4) 

⇒ N = 40 

∴ The no. of ways of selecting 3 boys and 3 girls is 40.