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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 from the lot.
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Solution
Given that bag contains 5 black and 6 red balls.
Number of ways of selecting 2 black balls out of 5 black balls = 5C2
And number of ways of selecting 3 red balls out of 6 red balls = 6C3
∴ Total number of ways of selecting 2 black and 3 red balls = 5C2 × 6C3
= `(5*4)/(2*1) xx (6*5*4)/(3*2*1)`
= 10 × 20
= 200 ways
Hence, the required ways of selecting the balls = 200.
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