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Question

The letters of the word "QUESTION" are arranged in a row at random. The probability that there are exactly two letters between Q and S is

A
114
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B
57
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C
17
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D
528
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Solution

The correct option is A 528
Word QUESTION has 8 letters
so total number of word can be formed are 8!
For exactly two letters between Q and S
Q_ _S_ _ _ _ , _ Q_ _S_ _ _, _ _ Q_ _S_ _ , _ _ _Q_ _S _, _ _ _ _Q_ _S
And similarly other 5 will be formed by interchanging Q and S
so total favourable outcomes=5*2*6!
Probability =5*2!*6!/8!=5/28

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