Question

The number of all four digit numbers which are divisible by 4 that can be formed from the digits 1, 2, 3, 4, and 5, is?
A. 125
B. 30
C. 25
D. None of these

Answer 1

Hint:
Here we will use the concept of permutation to solve the question. Permutation is a method of arranging objects from a given set of objects such that sequence or order of arrangement matters.

Complete step by step solution:
Here we need to find the number of four digit numbers that can be formed from these digits. We know, for any number to be divisible by 4, its last two digits should be divisible by 4.
Here repetitions are allowed, so we can use these digits any number of times.
The last 2 digits of the 4 digit numbers that can be formed using the given digits are 12, 24, 32, 44, and 52.
The number of ways in which we can arrange these digits for 1st and 2nd digits of 4 digit numbers are \[5 \times 5\].
Hence, the required number of four digit numbers that can be formed will be the product of the number of possible last two digits and the number of possible first two digits of 4 digit numbers.
Hence, the required number of 4 digit numbers divisible by 4 that can be formed using these digits \[ = 5 \times 5 \times 5 = 125\].

Hence, the correct option is option A.

Note:
The common mistake that occurs while solving these problems is that we forget the condition of repletion when it’s not written in the question. There are no restrictions in the given question that means repetition is allowed in the question. One more mistake that occurs is that we sometimes forget to add the number 44 for the last two digits.