# Find the number of permutations of letters of the following word: SHANTARAM - Mathematics and Statistics

Sum

Find the number of permutations of letters of the following word: SHANTARAM

#### Solution

The word SHANTARAM has 9 letters of which ‘A’ is repeated 3 times and the rest all are different.
Hence, the number of permutations

= ("n"!)/("p"!)

= (9!)/(3!)

= (9 xx 8 xx 7 xx 6 xx 5 xx 4 xx 3!)/(3!)

= 60480

Concept: Permutations - Permutations When All Objects Are 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 1. (ii) | Page 82