Can you count it?
Probability
Level
3
How many 4-digit positive integers have exactly one even digit?
The answer is 2375.
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1 solution
There are four cases:
Case 1: The first digit is even. We have four choices for the first digit, and five for each of the three for a total of ( 4 ) ( 5 ) ( 5 ) ( 5 ) = 5 0 0 .
Case 2: The second digit is even. We have five choices for each digit for a total of ( 5 ) ( 5 ) ( 5 ) ( 5 ) = 6 2 5 .
Case 3: The third digit is even. This case is the same as the second case. It has also a total of ( 5 ) ( 5 ) ( 5 ) ( 5 ) = 6 2 5 .
Case 3: The fourth digit is even. This case is the same as the second and third cases. It has also a total of ( 5 ) ( 5 ) ( 5 ) ( 5 ) = 6 2 5 .
So the final total is 5 0 0 + 6 2 5 + 6 2 5 + 6 2 5 = 2 3 7 5