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In how many ways can the letters of the word ‘PARALLEL’ be arranged so that all L’s do not come together?

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To find: number of words where L do not come together 

Let the three L’s be treated as a single letter say Z 

Number of words with L not the together = Total number of words - Words with L’s together 

The new word is PARAEZ 

Total number of words = \(\frac{8!}{213!}\) = 3360

Words with L together = 6! = 720

⇒ Words with L, not together = 3360 – 720 = 2640 

There are 2640 words where L do not come together

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