The total number of 3 digit numbers would be:

First digit can be 5 different ways (It can't be 0)
The second digit can also be 5 ways (it can be 0)
The last digit can be 4 ways.

5 5 4

5*5*4=100

100 Total 3 digit numbers using 0,1,2,3,4,5

Now the number of odd numbers: The ones digit is 1,3, or 5.

The first digit can be 4 different ways (it can't be 0 and can't be the odd digit that is the ones digit)
The second digit can be 4 different ways (it can be 0 but can't be the first digit or the odd digit that is the ones digit)
The last digit can be 3 different ways (1,3, or 5)

4 4 3

4*4*3=48

So there are 48 odd digits.

The number of even digits will be 100-48 = 52

52 even digits



4 4 3

Excellent, thanks, but the fact that "no digit should be repeated" should be different from the scenario in which any digit can be repeated. The solution provided looks the latter case.

muzali wrote:How many number of 3 digit numbers can be formed with the digits 0,1,2,3,4,5 if no digit is repeated in any number? How many of these are even and how many odd?

This clearly isn't a GMAT style question, since there are multiple questions built in and no answer choices.

Please clarify: can the first digit be 0? If we're building a code, we could definitely start with 0. If we're talking about the 3 digit numbers on the number line, then the first digit has to be 1 through 9 (or 1 through 5 in this particular question).

Is this just a question you made up because you're curious, or did you take it from somewhere?

Stuart Kovinsky wrote:

muzali wrote:How many number of 3 digit numbers can be formed with the digits 0,1,2,3,4,5 if no digit is repeated in any number? How many of these are even and how many odd?

This clearly isn't a GMAT style question, since there are multiple questions built in and no answer choices.

Please clarify: can the first digit be 0? If we're building a code, we could definitely start with 0. If we're talking about the 3 digit numbers on the number line, then the first digit has to be 1 through 9 (or 1 through 5 in this particular question).

Is this just a question you made up because you're curious, or did you take it from somewhere?

I was posed this question and was confused about how to approach it. It'd be great if you can explain the thought process for both the cases
1. 0 can be in the hundreds place
2. 0 cannot be in the hundreds place