In how many ways can the letters of the word ‘PENCIL’ be arranged so that N is always next to E?
Given: We have 6 letters
To Find: Number of ways to arrange letters P,E,N,C,I,L
Condition: N is always next to E
Here we need EN together in all arrangements.
So, we will consider EN as a single letter.
Now, we have 5 letters, i.e. P,C,I,L and ‘EN’.
5 letters can be arranged in
⇒
⇒
⇒ 120
In 120 ways we can arrange the letters of the word ‘PENCIL’ so that N is always next to E