The question is from Permutation and Combination. This is about Rearranging Letters. We need to find out the number of words that can be formed using the letters given in that particular word. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 16: In how many ways can letters the word ATTITUDE be rearranged such that no two Ts are adjacent to each other?

- 6720
- 2400
- 4320
- 1800

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ATTITUDE has 8 letters, of which 3 are Ts

Now, let us place the letters that are not Ts on a straight line. We have AIUDE. These can be arranged in 5! ways.

Now let us create slots between these letters to place the Ts in.

In order to ensure that no two Ts are adjacent to each other, let us create exactly one slot between any two letters.

A __ I __ U __ D __ E

Additionally, let us add one slot at the beginning and end as well as the Ts can go there also.

__A __ I __ U __ D __ E__

Now, out of these 6 slots, some 3 can be T. That can be selected in ^{6}C_{3} ways.

So, total number of words = 5! × ^{6}C_{3} = 2400.

The question is **"In how many ways can letters the word ATTITUDE be rearranged such that no two Ts are adjacent to each other?"**

Choice B is the correct answer.

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