Question

Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.

Answer 1

Total number of balls = 6 + 5 + 7 = 18
Number of red balls = 6
Number of green balls = 5
Number of blue balls = 7
9 balls are to be drawn, 3 of each Colour,
No. of ways of drawing 3 red balls out of 6 red balls = ⁶C₃
Similarly, No. of ways of drawing 3 green balls out of
5 green balls = ⁵C₃
No. of ways of drawing 3 blue balls out of
7 blue balls = ⁷C₃
∴ Total number of ways = ⁶C₃ × ⁵C₃ × ⁷C₃ 

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

=`(6xx5xx4xx3!)/(3xx2xx1xx3!)xx(5xx4xx3!)/(3!xx2)xx(7xx6xx5xx4!)/(3xx2xx1xx4!)`

= 20 × 10 × 35

= 7000