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Q.

How many different words can be formed from the letters of ‘CONSTANTINOPLE’ in which all three N come together?

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a

\frac{14!}{21 3! 2!}

b

\frac{12!}{21 2!}

c

\frac{12!}{21 3! 2!}

d

None of these

answer is B.

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Detailed Solution

The total number of letters in this word are 14.
The letter N is repeated 3 times, the letter O is repeated 2 times and the letter T is repeated 2 times.
After taking all three N together, the number of letters left in the word ‘CONSTANTINOPLE’ is 11.
So now, the total letters in the word ‘CONSTANTINOPLE’ are 1 + 11 = 12.
Number of the words that can be formed from the letters of ‘CONSTANTINOPLE’ in which all three N come together is

\frac{12!}{21 2!}

.

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