# How many words can be formed with the letters of the word 'PARALLEL'

Question:

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

Solution:

The word PARALLEL consists of 8 letters that include two As and three Ls.

Total number of words that can be formed using the letters of the word PARALLEL $=\frac{8 !}{2 ! 3 !}=3360$

Number of words in which all the Ls come together is equal to the condition if all three Ls are considered as a single entity.

So, we are left with total 6 letters that can be arranged in $\frac{6 !}{2 !}$ ways (divided by $2 !$ since there are two As), which is equal to 360 .

Number of words in which all Ls do not come together = Total number of words - Number of words in which all the Ls come together

$=3360-360$

$=3000$