In how many ways can the letters of the word ‘PENCIL’ be arranged

1.	In how many ways can the letters of the word ‘PENCIL’ be arranged so that I is always next to L.
Answer» There are 6 letters in the word ‘PENCIL’ Consider LI as one letter. Now 5 Letters (P,E,N,C,I,L) can be arranged in\(^5P_5=5! =120\) ways. Hence, the total number of ways in which I is always next to L is 120.

In how many ways can the letters of the word ‘PENCIL’ be arranged so that I is always next to L.

Answer»

There are 6 letters in the word ‘PENCIL’

Consider LI as one letter. Now 5 Letters (P,E,N,C,I,L) can be arranged in\(^5P_5=5! =120\) ways.

Hence, the total number of ways in which I is always next to L is 120.