Class 11

Math

Algebra

Permutations and Combinations

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

$3$ boys can be selected from $5$ boys In $_{5}C_{3}$ ways.

$3$ girls can be selected from $4$ girls In $_{4}C_{3}$ ways.

Therefore, by multiplication principle, number of ways in which a team of $3$ boys and $3$ girls can be selected

$_{5}C_{3}×_{4}C_{3}=3!2!5! ×3!1!4! $

$=3!×25×4×3! ×3!4×3! $

$=10×4$

$=40$