# How many 3 digit even numbers can we form with numbers from $\{0,1,2,3,4,5,6,7 \}$?

How many 3 digit even numbers can we form with numbers from $$\{0,1,2,3,4,5,6,7 \}$$?
My work : We have to count numbers of the form $$\overline{abc}$$.
$$a$$ can take $$7$$ values, $$b$$ can take $$8$$ values and $$c$$ can take $$4$$ values.Hence, there are $$7\times 8 \times 4=224$$ numbers. Is this correct?
EDIT: It seems that my answer is correct. Now, how to count the numbers if I am not allowed to repeat digits?

• Assuming you're allowed to repeat digits, this is correct. – Austin Mohr Mar 19 at 17:27
• @AustinMohr Thank you! I am allowed to repeat digits, but I wonder, how should I have approached this if I weren't? – ChemistryGeek Mar 19 at 17:32
• If you are not allowed to repeat digits, choose the units digit first and distinguish between the case in which it is $0$ (in which case, you are free to fill the hundreds digit with any of the other digits) and the case in which it is nonzero (in which case, the hundreds digit may not be the units digit or the $0$). – N. F. Taussig Mar 19 at 17:35