# How many four digit numbers can be formed using the digits 1,2,3,4,5 but with repetition that are divisible by 4?

2
by nivetangeli

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by nivetangeli

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So here we can have four types of numbers

(4) ab44

where a,b can be any digit from 1,2,3,4,5

So now we have to choose 2 digits from 5 digits,

Now,

So total

We have four types of numbers so

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The number all numbers with 4 digits and each digits can be 1 to 5 with repetition will be equal to : 5 * 5 * 5 * 5 = 625 as each digit can be any of 1 to 5.

We want those numbers which are divisible by 4. Numbers ending in 12, 24, 32, 44, 52 are all divisible by 4.

The first digits can be any digit with repetition. So number of ways of choosing first two digits are 5*5 = 25.

Number of ways of choosing last two digits are : 5 combinations mentioned above.

The total = 5*25 = 125.

We want those numbers which are divisible by 4. Numbers ending in 12, 24, 32, 44, 52 are all divisible by 4.

The first digits can be any digit with repetition. So number of ways of choosing first two digits are 5*5 = 25.

Number of ways of choosing last two digits are : 5 combinations mentioned above.

The total = 5*25 = 125.