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

Sum

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

#### Solution

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.

Concept: Concept of Permutations - Permutations When Repetitions Are Allowed
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.3 | Q 6. (iv) | Page 81