How many different words can be formed using all the letters of the word $^{'} {ALLAHABAD}^{'}$ when both $L^{'} s$ are not together

4200

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5812

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6000

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5250

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Solution

The correct option is B $4200$
$A L L A H A B A D$
Total number of words $= \frac{9!}{4! \times 2!} = 7560$
Concider both L's as $1$ identity
Number of such words $= \frac{8!}{4!} \times 2 = 3360$ Ways
Number of words in which L's are not together
=Total number of words $-$ Words with $L$ are together
$= 7560 - 3360$
$= 4200$
Therefore number of possiblities $= 4200$

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Similar questions

^{'} A L L A H A B A D^{'}

(i) How many different words can be formed by using all the letters of the word, 'ALLAHABAD'?

In how many of them :

(ii) Both L's do not come together ?

(iii) The vowels occupy the even positions ?

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

L

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