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Question

A letter is selected from each of the words MATHEMATICS and STATISTICS. The probability that the same letter is selected is ab, then a+b+3 (where a and b are co-prime) is divisible by

A
3
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B
5
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C
7
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D
13
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Solution

The correct options are
A 5
B 13
Number of letters in MATHEMATICS=11
The probability to choose any one letter =111
Similarly, the probability to choose any one letter for SATISTICS =110
Now, the common letters are A,T,I,C,S
The probability of choosing same letter =211×110+211×310+111×210+111×110+111×310
=14110=755
a+b+3=7+55+3=65

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