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Sum

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

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#### 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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