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Q.

A fair die is thrown 20 times. The probability that on the 10th throw, the fourth six appears is

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a

20C10×56/620

b

120×57/610

c

84×56/610

d

none of these

answer is C.

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Detailed Solution

In the first 9 throws, we should have three sixes and six non-sixes; and a six in the 10th throw, and thereafter it does not matter whatever face appears. So, the required probability is 9C3163×566×16×1×1×1×⋯×110 times=84×56610
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A fair die is thrown 20 times. The probability that on the 10th throw, the fourth six appears is