# How Many Words Can Be Formed with the Letters of the Word 'Parallel' So that All L'S Do Not Come Together? - Mathematics

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

Concept: Factorial N (N!) Permutations and Combinations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Exercise 16.5 | Q 5 | Page 43