Question

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

Answer 1

If number is divisible by 4, then rule says, last two digits must be divisible by 4,

So here we can have four types of numbers
(1) ab12
(2) ab24
(3) ab32
(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,
(1) a can be chosen in 5 ways.
(2) b can be chosen in 5 ways.

So total no. of ways choosing a and b = 5 * 5 = 25

We have four types of numbers so total no. = 4 * 25 = 50

Answer
100

Answer 2

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.