Question

Find the number of ways so that letters of the word HISTORY can be arranged as Y and T are together

Answer 1

In the word 'HISTORY', the number of letters is n = 7.

Words in which Y and T are together:

Since Y and T are always together, consider them as a single unit.

Now we have 1 + 5 = 6 different letters, that can be arranged in ⁶P₆ ways.

After this is done Y and T can be arranged amongst themselves in ²P₂ ways.

Hence, the total number of words formed in which Y and T are together is given by

⁶P₆ × ²P₂ = 6! × 2!

= 6 × 5 × 4 × 3 × 2 × 1 × 2 × 1

= 720 × 2

= 1440