The number of 6 digits numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated, is:

Options

A. 60
B. 72
C. 48
D. 36

Answer

A

Explanation

Given six digits are 0,1,2,5,7 and 9
If [(sum of odd palce digit)-(even places digit)] is divisible by 11, then the given number is divisible by 11.
Let one such type of number is a b c d e f
Then |(a+c+e)-(b+d+f)| must be divisible by 11.
It is possible if a,c, `e in {2,1,9}` and b,d,f `in`{0,5,7}
Now we can arrange the given digit in `3! xx 2! xx 2!-2! xx 3!=60`