# Determine the number of arrangements of letters of the word ALGORITHM if no two vowels are together - Mathematics and Statistics

Sum

Determine the number of arrangements of letters of the word ALGORITHM if no two vowels are together

#### Solution

In the word 'ALGORITHM' the number of letters is n = 9.

No two vowels are together:

Consider one of the possible arrangements of V (vowels) and C (consonants)

VCVCVCVCVCVCV

Here, there are 7 positions for vowels and 6 positions for consonants.

∴ 3 vowels can be arranged in 7P3 ways and 6 consonants can be arranged in 6P6 ways.

Hence, the total number of words in which no two vowels are together

= 7P3 × 6P6

= (7!)/(4!) xx 6!

= 7 × 6 × 5 × (6 × 5 × 4 × 3 × 2 × 1)

= 210 × 720

= 151200

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

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 3 Permutations and Combination
Exercise 3.3 | Q 6. (b) | Page 55