Question

Find the number of distinct words formed from letters in the word INDIAN. How many of them have the two N’s together?

Answer 1

In the word 'INDIAN', the number of letters is n = 6 of which I repeats twice, i.e., p = 2, N repeats twice, i.e., q = 2, and the rest are distinct.

∴ the number of different words formed with letters of the word INDIAN

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

= `(6!)/(2!2!)`

= `(6 xx 5 xx 4 xx 3 xx 2!)/(2 xx 1 xx 2!)`

= 180

Two N's are together:

Two N's form 1 unit and with the remaining 4 letters we have 5 letters in which I repeat twice.

∴ the number of different words formed in which two N's are together

= `(5!)/(2!)`

= `(5 xx 4 xx 3 xx 2!)/(2!)`

= 60