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Question
If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then, the probability that the drawn balls are of different colours is:
Options
`1/66`
`3/66`
`19/66`
`47/66`
Solution
`47/66`
Explanation:
Given, Number of white balls = 3
Number of Black balls = 4
Number of Red balls = 5
Total no. of balls (ways) = 12
Total no. of ways of drawing 2 balls out of 12 balls
= 12C2
= `(12!)/(10!2!)`
= 66
Total no. of ways of drawing 2 balls of different colours
= 1 white 1 black + 1 black 1 red + 1 red 1 white
= 3C1 × 4C1 + 4C1 × 5C1 + 5C1 × 3C1
= 3 × 4 + 4 × 5 + 5 × 3
= 47
So, the probability of drawing 2 balls of different colours
= `47/66`
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