Question

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

Answer 1

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 = ⁶P₆ = 6!
Also, ‘Y’ and ‘T’ can be arranged among themselves in ²P₂ 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.