# Find the number of arrangements of letters in the word CONSTITUTION that begin and end with N. - Mathematics and Statistics

Sum

Find the number of arrangements of letters in the word CONSTITUTION that begin and end with N.

#### Solution

There are 12 letters in the word CONSTITUTION, in which ‘O’, ‘N’, ‘I’ repeat two times each, ‘T’ repeats 3 times.
The arrangement starts and ends with ‘N’, 10 letters other than N can be arranged between two N, in which ‘O’ and ‘I’ repeat twice each and ‘T’ repeats 3 times.
∴ Total number of arrangements with the letter N at the beginning and at the end = (10!)/(2!2!3!)

Concept: Permutations When All Objects Are Not Distinct
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.4 | Q 9 | Page 83