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 _____.

Step-by-step solution

Digits given are 1 , 2 , 3 , 4 , 5 , 7 , 9 Now multiple of 11 → Difference of sum at even & odd place should be divisible by 11 . Let number of the form a b c d e f g ∴   a + c + e + g - b + d + f = 11 x a + b + c + d + e + f = 31 ∴ either a + c + e + g = 21 or 10 ∴ b + d + f = 10 or 21 Case-1 a + c + e + g = 21 b + d + f = 10 b , d , f ∈ 1 , 2 , 7 2 , 3 , 5 1 , 4 , 5 a , c , e , g ∈ 1 , 4 , 7 , 9 , 3 , 4 , 5 , 9 , 2 , 3 , 7 , 9 ∴ Total number in case-1 = 3 ! × 3