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Question

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is

A
122
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B
322
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C
291
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D
277
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Solution

The correct option is C 291
Let S be the sample space.
Then, n(S) = number of ways of drawing 3 balls out of 15
=15C3
=(15×14×13)(3×2×1)
=455
Let E = event of getting all the 3 red balls.
n(E)=5C3=5C2=(5×4)(2×1)=10
P(E)=n(E)n(S)=10455=291

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