Question

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

SHANTARAM

Answer 1

In the word 'SHANTARAM', the number of letters is n = 9 of which A repeats thrice, i.e., p = 3 and rest are distinct.

∴ the number of distinct permutations of the letters

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

= `(9!)/(3!)`

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

= 9 × 8 × 7 × 6 × 5 × 4

= 60480.