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Q.

Words from the letters of the word PROBABILITY are formed by taking all letters at a time. The probability that both .B's are not together and both I's are not together is

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a

5255

b

5355

c

5455

d

none of these

answer is B.

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Detailed Solution

The total number of cases is 11!(2! x 2!). The number of favorable cases is [11!(2! x 2!)] - 9! Therefore, the required probability is=1−9!×411!=5355
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Words from the letters of the word PROBABILITY are formed by taking all letters at a time. The probability that both .B's are not together and both I's are not together is