Question

How many five-digit multiples of $11$ are there, if the five digits are $3,4,5,6$ and $7$ same order?

• A. $12$
• B. $13$
• C. $10$
• D. None of these

Answer 1

The correct option is A $12$

A number is divisible by 11, if the difference between the sum of digits at even places and odd places is either 0 or divisible by $11$.
Numbers $5,3,6,4,7$ is a multiple of $11$.

The number at odd places $5,6,7$ can be arranged in $3!$ ways and $3,4$ can be arranged in $2!$ ways.
Therefore, total number of ways of such numbers $=3!\times 2!=12$.