Question:
In how many ways can the letters of the word ‘PENCIL’ be arranged so that N is always next to E?
Solution:
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 ${ }^{5} P_{5}$ ways
$\Rightarrow{ }^{5} P_{5}$
$\Rightarrow \frac{5 !}{(5-5) !}$
$\Rightarrow \frac{5 !}{0 !}$
$\Rightarrow 120$
In 120 ways we can arrange the letters of the word ‘PENCIL’ so that N is always next to E
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