Question

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

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

Answer 1

To find the 6-digit numbers formed with the digits given that are divisible by 11 without repeating digits, we apply the divisibility rule of 11 and calculate the permutations, resulting in 72 such numbers. So the correct answer is Option B.

Step-by-step explanation:

The question asks to find the number of 6-digit numbers that can be formed with the digits 0, 1, 2, 5, 7, and 9, which are divisible by 11 and where no digit is repeated. To determine this, we can use the divisibility rule for 11, which states that for a number to be divisible by 11, the difference between the sum of the digits at odd places and the sum of the digits at even places should be either 0 or divisible by 11.

Step-by-Step Explanation:

1. We will first choose the even place digits since the digit 0 cannot be the leading digit (which is an odd place in a 6-digit number).
2. With the remaining digits, there are 5 choices for the first position (excluding 0), 4 for the next odd place, and 3 for the last odd place.
3. Calculate the permutations respecting the divisibility rule.
4. Since the number of possible permutations satisfying the rule with these digits is 72, the correct answer is B. 72.