Question

Determine the number of arrangements of letters of the word ALGORITHM if O is the first and T is the last letter.

Answer 1

A word is to be formed using the letters of the word ALGORITHM.
There are 9 letters in the word ALGORITHM.
When beginning with O and ends with T:
All the letters of the word ALGORITHM are to be arranged among themselves such that arrangement begins with O and ends with T.
7 letters other than O and T can be filled between O and T in ⁷P₇ i.e., 7! ways = 5040 ways.
∴ 5040 words beginning with O and ending with T can be formed.