Question

Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 8 green balls, and 7 blue balls so that 3 balls of every colour are drawn

Answer 1

9 balls are to be selected from 6 red, 8 green, 7 blue balls such that the selection consists of 3 balls of each colour.

∴ 3 red balls can be selected from 6 red balls in ⁶C₃ ways.

3 green balls can be selected from 8 green balls in ⁸C₃ ways.

3 blue balls can be selected from 7 blue balls in ⁷C₃ ways.

∴ Number of ways selection can be done if the selection consists of 3 balls of each colour

= ⁶C₃. ⁸C₃. ⁷C₃

= `(6!)/(3!3!) xx (8!)/(3!5!) xx (7!)/(3!4!)`

= `(6 xx 5 xx 4 xx 3!)/(3 xx 2 xx 1 xx 3!) xx (8 xx 7 xx 6 xx 5!)/(3 xx 2 xx 1 xx 5!) xx (7 xx 6 xx 5 xx 4!)/(3 xx 2 xx 1 xx 4!)`

= 20 × 56 × 35

= 39200