Question

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

Answer 1

When ‘R’ is taken thrice, ‘S’ is taken twice and ‘T’ is taken 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!)/(2 xx 1 xx 2 xx 1 xx 3!)`

= 7 × 6 × 5

= 210

∴ 210 different words can be formed when the letter R is used thrice and letters S and T are used twice each.