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Question
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
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Solution
Ways to select 2 balls out of 5 black balls = 5C2
Ways to select 3 balls out of 6 red balls = 6C3
Total ways of selecting 2 black and 3 red balls out of 5 black and 6 red balls.
=5C2 × 6C3
= `(5!)/(2!3!) xx (6!)/(3!3!)`
= `(5 xx 4)/(2) xx (6 xx 5 xx 4)/(3 xx 2 xx 1)`
= 10 x 20
= 200
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