Questionbank: Permutation and Probability

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To answer this one, you should first know the number of arrangements in which the T's are together!!

ReArranging Letters

In how many ways can letters the word ATTITUDE be rearranged such that no two Ts are adjacent to each other?
1. 6720
2. 2400
3. 4320
4. 1800

Choice B. 2400

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Detailed Solution

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 6C3 ways.

So, total number of words = 5! × 6C3 = 2400

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