Question

How many 5-digit numbers divisible by 11 are there containing each of the digits 2, 3, 4, 5, 6?

Answer 1

A number is divisible by 11 if the difference between the sum of the digits at even places and the sum of the digits at odd places is divisible by 11.

The numbers formed by 2, 3, 4, 5 and 6 will be divisible by 11 if 2, 3 and 5 are filled at odd places and 4 and 6 are filled at even places.

Thus, the different numbers are:

2 4 3 6 5	3 4 2 6 5	5 4 2 6 3
2 4 5 6 3	3 4 5 6 2	5 4 3 6 2
2 6 3 4 5	3 6 2 4 5	5 6 2 4 3
2 6 5 4 3	3 6 5 4 2	5 6 3 4 2

Hence, the number of 5-digit numbers containing the given digits and divisible by 11 is 12.