Question

How many four digit numbers that are divisible by four can be formed using 0 to 7?

Answer 1

Hey mate here's your answer

We can use digits from 0 to 7only. Following are the possibilities.

04, 12, 16, 20, 24, 32, 36, 40, 52, 56, 60, 62, 64 - total 13

A number can’t start with zero, therefore cases above having a 0, will have to be dealt separately.

04,20,40,60 - 4possibilities

For first 2 digits we can use product rule to get 6 × 5=30. Because, out of 8digits 2 have been already used up. So, in all, there are 30×4=120possibilities.

For the remaining 9 cases, the first 2digits can be chosen in 5×5=25 Because, out of remaining 6digits, we can’t choose 0 as the starting digit. So, there are 25 ×9=225

So, combining the above cases, we get the answer to be 120+225=345.

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