In how many ways can the letters of the word pencil be arranged so that n is always next to e


There are 6 letters in the word ‘PENCIL’.

(1)

Consider EN as one letter. Now 5 letters (P, C, I, L, EN) can be arranged in 5P5 = 5! = 120 ways.

Hence, total number of ways in which N is always next to E is 120.

(2)

Consider EN as one letter. Now, 5 letters can be arranged in 5P5 = 5! = 120 ways

E and N can arrange among themselves in 2! = 2 ways.

Hence, the total number of ways in which N and E are always together = 120 × 2 = 240.

In how many ways can the letters of the word ‘PENCIL’ be arranged so that N is always next to E? be arranged so that N is always next to E?

In how many ways can the letters of the word pencil be arranged so that n is always next to e

In how many ways can the letters of the word pencil be arranged so that n is always next to e

Text Solution

Solution : (1) If we keep letter N always next to E then they(EN) treated as 1 letter, so we have total 5 letters now then we have by formula the number of ways of arrangement is`5!`<br> `\Rightarrow 120`ways<br> (2) If E and N are always togather then we have number of ways of arrangement<br> `5!\times 2!`<br> `\Rightarrow 240`ways<br>