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Sum

Find the number of ways letters of the word HISTORY can be arranged if Y and T are together.

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#### Solution

There are 7 letters in the word HISTORY

When ‘Y’ and ‘T’ are together.

Let us consider ‘Y’ and ‘T’ as one unit

This unit with the other 5 letters is to be arranged.

∴ The number of arrangements of one unit and 5 letters = ^{6}P_{6} = 6!

Also, ‘Y’ and ‘T’ can be arranged among themselves in ^{2}P_{2} i.e., 2! ways.

∴ Total number of arrangements when Y and T are always together = 6! × 2! = 720 × 2 = 1440

∴ 1440 words can be formed if Y and T are together.

Concept: Permutations - Permutations When Repetitions Are Allowed

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