Question

The number of numbers of four different digits that can be formed from the digits of the number 12, 356 such that the numbers are divisible by 4, is
A. 36
B. 48
C. 12
D. 24

Answer 1

Hint: Here, we will first find the combinations of the last two digits from the given numbers and then calculate the permutation to find the number of ways for the first two digits. Then we will find the number of numbers by finding the product of the number of ways in both cases.

Complete step-by-step solution:
Given that the number is 12,356.
We know that for a number to be divisible by 4, the last two digits must be divisible by 4 using the divisibility rule of 4.

So, the combinations of the last two digits from the above number having digits 1, 2, 3, 5, 6 which are divisible by 4 is 12, 32, 52, 16, 36, 56.

We find the number of ways for the first two digits is to be selected from the remaining 3 digits by finding the permutations.

\[{}^3{{\text{P}}_2} = 6{\text{ ways}}\]

So we get from above that there are six such cases with different last two digits.

Find the total number of numbers.

\[6 \times 6 = 36\]

Thus, the number of numbers of four different digits that can be formed from the digits of the given number is 36.

Hence, the option A is correct.

Note: In this question, some students write the formula of combination for permutation, which is wrong. Students should also know the concept of permutations and combinations before solving this question. Also, we are supposed to write the values properly to avoid any miscalculation.