3 digit numbers

[muzali]

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?

[dmateer25]

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

[muzali]

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.

[Stuart@KaplanGMAT]

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?

[muzali]

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