Question

How many different words can be formed using all the letters of the word “ALLAHABAD” when both ”L” are not together
    (A) 4200
    (B) 5812
    (C) 6000
    (D) 5250

Answer 1

Hint: In the above question of permutation we will first calculate total the number of words by rearrangement , then we will calculate the number of words that can be formed when both “L” are together and the difference of total words and the words when both “L” are together gives the number of words having both “L” not together.

Complete step-by-step answer:
Now, we have the word ALLAHABAD, in which there are total 9 letters with four A and two L, so the total words that can be formed by rearrangement of the letters are as follow,
Total number of words = $\dfrac{9!}{4!\times 2!}=7560$
Now, let us consider that both the “L” as one identity.
Number of such words = \[\dfrac{8!}{4!}\times 2\] = 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 the correct option of the question is option A.

Note: Here, considering both the letters of L as one set will make the problem easier to solve. Also remember that, we can find the required favourable outcomes by subtracting the non-favourable number of outcomes from the total number of outcomes.