Question

1, 2 , 3, 4 digits are available. How many number of 4 digited numbers which are divisible by 4. (There should be no repetition of digits in the numbers) can be formed?

Answer 1

I thinks that it may be 2298

Answer 2

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Here, we've to find the no. of numbers which are divisible by 4.

A number is divisible by 4 if and only if the number made by the last two digits of that number is divisible by 4.

E.g.: 24235364 is divisible by 4 because the number formed by last two digits, 64, is a multiple of 4.

Okay, let's find the answer.

We've to find the no. of multiples of 4 formed by the digits 1, 2, 3 and 4 without digit repetition.

So first of all, we've to find the no. of possibilities of the nos. formed by the last two digits of these 4 digit numbers.

Which means, in how many ways the last two digits become a multiple of 4 using these digits without repetition.

Okay, the possibilities are given below:

12, 24, 32.

So there are three types of numbers. The no. of numbers each type contain will be same.

44 can also be if repetition occurs!

Okay, now let's find the following:

First let's find the no. of numbers which end in 12.

As it ends in 12, the other digits should be 3 and 4. So the answer is 2! = 2.

So there are 2 numbers ending in 12. So are 24 and 32.

So the no. of four digit multiples of 4 that can be formed by using the digits 1, 2, 3 and 4 without digit repetition is 2 × 3 = 6.

And those 6 numbers are as follow:

3412, 4312, 1324, 3124, 1432, 4132

Hope my article may help you.

Please mark it as the brainliest if it helps.

Please ask me if any doubt.

Thank you. :-))