How many 4digit numbers less than 6000 are there with distin

How many 4-digit numbers less than 6000 are there with distinct digits that have a remainder of 0 when divided by 5.

Solution

Divided by 5.......that means first digit should be either 0 or 5

And   less than 6000 that means last digit shoud be 0,1,2,3,4,5

All the digits should be different

Case 1------first digit is 0

\"0\"

total ways for case 1 = 5*8*7=280

Case 2-----first digit is 5

\"5\"

total ways for case 2 = 5*8*7=280

Case 3 = Number 6000 also a case

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total number of ways=280+280+1=561