# How many different words are formed if the letter R is used thrice and letters S and T are used twice each? - Mathematics and Statistics

Sum

How many different words are formed if the letter R is used thrice and letters S and T are used twice each?

#### Solution

When R is used thrice, S is used twice and T is used twice,
∴ Total number of letters available = 7, of which S and T repeat 2 times each, R repeats 3 times.
∴ Required number of arrangements = (7!)/(2!2!3!)

= (7 xx 6 xx 5 xx 4 xx 3!)/(2xx1xx2xx1xx3!)

= 7 × 6 × 5
= 210
∴ 210 different words can be formed with the letter R is used thrice and letters S and T are used twice each.

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 7 | Page 82