Question

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

Answer 1

Hint: Here we have to select 3 boys and 3 girls from 5 boys and 4 girls. Thus the concept of combinations is applied.

Complete step-by-step answer:
Now a team of 3 boys and 3 girls is to be formed in total we have 5 boys and 4 girls
Now the number of ways of selecting 3 boys from a total of 5 boys is ${}^5{C_3}$
Now the number of ways of selecting 3 girls from a total of 5 girls is ${}^4{C_3}$
Now the total ways in which a team of 3 boys and 3 girls be formed is
${}^5{C_3} \times {}^4{C_3}$(Multiplication principle)
Using $\dfrac{{n!}}{{r!\left( {n - r} \right)!}} = {}^n{C_r}$
We have $\dfrac{{5!}}{{2!3!}} \times \dfrac{{4!}}{{3!1!}} = \dfrac{{5 \times 4 \times 3!}}{{2 \times 3!}} \times \dfrac{{4 \times 3!}}{{3!}} = 10 \times 4 = 40$
Hence, there are 40 ways.

Note: We are applying the concept of combinations (${}^n{C_r}$) here because we are only concerned with selecting members for the team and not the order in which they are selected.