Question

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

• A. $4200$
• B. $5812$
• C. $6000$
• D. $5250$

Answer 1

Answer: (A)

$4200$

$ALLAHABAD$

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 $=4200$