# Determine the number of arrangements of letters of the word ALGORITHM if vowels are always together. - Mathematics and Statistics

Sum

Determine the number of arrangements of letters of the word ALGORITHM if vowels are always together.

#### Solution

A word is to be formed using the letters of the word ALGORITHM.
There are 9 letters in the word ALGORITHM.
When vowels are always together:
There are 3 vowels in the word ALGORITHM. (i.e., A, I, O)
Let us consider these 3 vowels as one unit.
This unit with 6 other letters is to be arranged.
∴ It becomes an arrangement of 7 things which can be done in 7P7 i.e., 7! ways and
3 vowels can be arranged among themselves in 3P3 i.e., 3! ways.
∴ Total number of ways in which the word can be formed= 7! × 3! = 30240
∴ 30240 words can be formed if vowels are always together.

Concept: Permutations - Permutations When Repetitions Are Allowed
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Chapter 6: Permutations and Combinations - Exercise 6.3 [Page 81]

#### APPEARS IN

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