Question

Find the number of ways so that letters of the word HISTORY can be arranged as begin and end with vowel

Answer 1

There are 7 letters in the word HISTORY

When begin and end with vowel

there are 2 vowels in the word HISTORY

All other letters of the word HISTORY are to be arranged between 2 vowels such that arrangement begins and ends with vowel.

Other 5 letters can be filled between the two vowels in ⁵P₅ i.e., 5! Ways

Also, 2 vowels can be arranged among themselves in ²P₂ i.e., 2! Ways

∴ total number of arrangements when the word begins and ends with vowel

= 5! × 2!

= 120 × 2

= 240

∴ 240 words can be formed if the arrangement begins and ends with vowel.