Question

The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is _____.

Answer 1

Sum of all given numbers = 31

Fig.

Difference between odd and even positions must be 0, 11 or 22, but 0 and 22 are not possible.
Therefore , Only difference 11 is possible
This is possible only when either 1, 2, 3, 4 is filled in odd position in some order and remaining in other
order. Similar arrangements of 2, 3, 5 or 7, 2, 1 or 4, 5, 1 at even positions.
∴ Total possible arrangements = (4! × 3!) × 4
= 576