Question

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

Answer 1

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 ⁵P₅ ways

⇒ ⁵P₅

⇒ \(\frac{5!}{(5-5)!}\) 

⇒ \(\frac{5!}{0!}\)

⇒ 120

In 120 ways we can arrange the letters of the word ‘PENCIL’ so that N is always next to E.