Question

The number of 6 digit 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:
1. 72
2. 60
3. 48
4. 36

Answer 1

Correct Answer - Option 2 : 60

The given 6 digits are 0, 1, 2, 5, 7, 9

Let’s take the numbers as,

a b c d e f

We know that, a number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or number divisible by 11.

i.e. (a + c + e) – (b + d + f) = 0 or Multiples of 11

The sum of all the digits is

0 + 1 + 2 + 5 + 7 + 9 = 24

Now,

(0 + 5 + 7) – (2 + 1 + 9) = 0

⇒ 12 – 12 = 0

Number of ways to arranging them

⇒ (3! × 3! × 2) – 1 (3! × 2!)

= (6 × 6 × 2) – 1(6 × 2)

= 72 – 12 = 60