Question

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

Answer 1

There are 6 letters in the word INDIAN in which I and N repeat twice.
Number of different words that can be formed using the letters of the word INDIAN

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

= `(6 xx 5 xx 4 xx 3 xx 2!)/(2xx2!)`
= 180
∴ 180 different words can be formed with the letters of the word INDIAN.
When two N’s are together.
Let us consider the two N’s as one unit.
They can be arranged with 4 other letters in
= `(5!)/(2!)`

= `(5 xx 4 xx 3 xx 2!)/(2!)`
= 60 ways
∴ 2 N can be arranged in 1 way
∴ Total number of arrangements = 60 × 1 = 60 ways
∴ 60 words are such that two N’s are together