Class 11

Math

Algebra

Permutations and Combinations

Find the number of ways of selecting $9$ balls from $6$ red balls, $5$ white balls and $5$ blue balls if each selection consists of $3$ balls of each colour.

$9$ balls have to be selected in such a way that each selection consists of $3$ balls of each colour.

Here,

$3$ balls can be selected from $6$ red balls in $_{6}C_{3}$ ways.

$3$ balls can be selected from $5$ white balls in $_{5}C_{3}$ ways.

$3$ balls can be selected from $5$ blue balls in $_{5}C_{3}$ ways.

Thus, by multiplication principle, required number of ways of selecting $9$ balls

$_{6}C_{3}×_{5}C_{3}×_{5}C_{3}=3!3!6! ×3!2!5! ×3!2!5! $

$=3!×3×2×16×5×4×3! ×3!×2×15×4×3! ×3!×2×15×4×3! $

$=20×10×10$

$=2000$