How many words can be formed with the letters of the word ‘PARALLEL’ so that all L’s do not come together?

Given:

The word

   

There are

   

letters in the word

   

out of which

   

and the rest all are distinct.

So by using the formula,

   

total number of arrangements

   

   

   

Or,

   

   

Now, let us consider all

   

together as one letter, so we have

   

letters out of which

   

repeats

   

times and others are distinct.

These

   

letters can be arranged in

   

Ways.

The number of words in which all L’s come together

   

   

Or,

   

   

So, now the number of words in which all

   

do not come together = total number of arrangements – The number of words in which all L’s come together