How good is your divisibility ?

Discrete Mathematics Level pending

Let \(\alpha\) be the number of 5 digit numbers divisible by 4 that can be formed using the digits \(0,1,2,3,4,5\) when repetition of digits is not allowed.

Let \(\beta\) be the number of 5 digit numbers divisible by 4 that can be formed using the digits \(0,1,2,3,4,5\) when repetition of digits is allowed.

Find the value of \(\alpha+\beta\) ?

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