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:
Correct Answer: Option A
Let S be the sample space.
Then, n(S) = number of ways of drawing 3 balls out of 15 = 15c3
\(\frac{15\times14\times13}{3\times2\times1}\) = 455.
Let E = event of getting all the 3 red balls.
n(E) = 5c3
= \(\frac{5\times4}{2\times1}\) = 10.
=> P(E) = n(E)/n(S) = 10/455 = 2/91.
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