Question

Find the number of ways so that letters of the word HISTORY can be arranged as Y is next to T

Answer 1

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 arrangments 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.