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Question
Find the number of ways letters of the word HISTORY can be arranged if Y is next to T.
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Solution
There are 7 letters in the word HISTORY
When ‘Y’ is next to ‘T’
Let us take this (‘Y’ next to ‘T’) as one unit.
This unit with 5 other letters is to be arranged.
∴ The number of arrangements of 6 letters and one unit = 6P6 = 6!
Also ‘Y’ has to be always next to ‘T’.
So they can be arranged in 1 way.
∴ Total number of arrangements possible when Y is next to T = 6! ×1 = 720
∴ 720 words can be formed if Y is next to T.
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