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Question

The number of selections of 6 different letters that can be made from the words NISHIT and RAHUL so that each selection consists of 3 letters from each word, is

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Solution

Here H is the common letter in words NISHIT and RAHUL
Now, for selecting six different letters, we must select H either from word RAHUL or from word NISHIT.

Hence, for the possible selections, we have
Case 1: H included in RAHUL (excluded inNISHIT)
Number of selections =4C24C3

Case 2: H excluded in RAHUL (no constraint in NISHIT)
Number of selections =4C35C3

Total count =4C24C3+4C35C3
=24+40=64

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