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Form 4 digit numbers using $\{1,2,3,4,5\}$
a) In some of the numbers, digits are distinct.
b) The number is even.
Solve for just $a$, just $b$, and for both $a$ and $b$.

I could not understand what is meant in part $a$. Is not it same with the set of all $4$ digit numbers written with $\{1,2,3,4,5\} = 5 \cdot 5 \cdot 5 \cdot 5$?

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I take it to mean, there are a lot of $4$-digit numbers you can form from $1,2,3,4,5$; some of them use the same digit more than once (for example, 1231), and some of them don't (for example, 4153); we want the ones that don't. – Gerry Myerson Feb 19 '13 at 0:52
@gnometorule it is the combinatorics class and we are currently only considering integer numbers. but I could not understand the meaning of the "some" either. – alev Feb 19 '13 at 0:57

$(a)$ asks you to find $4$-digit numbers with digits in $\{1,2,3,4,5\}$ for which the digits are distinct, i.e. 1234 or 3245, and $(b)$ wants you to find even $4$-digit numbers with digits in $\{1,2,3,4,5\}$, i.e. 2344 or 5432. Then it wants you to find even 4-digit numbers with distinct digits, i.e. 5412.

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But then, what is the use of the word "some"? Some does not mean all, right? – alev Feb 19 '13 at 0:59
Well, I guess it could mean to form sets of them that have at least one number with distinct digits. – Alexander Gruber Feb 19 '13 at 1:03
@alev Oh- here's an idea. Maybe some should be sum- so it would mean to form $4$-digit numbers for which the sum of the digits has distinct digits. – Alexander Gruber Feb 19 '13 at 1:08
I do no have an idea. Instructor wrote it without looking to a book. It was the first question of the lecture and I guess he underestimated this question and did not even want to waste time with question and gave it as a homework. – alev Feb 19 '13 at 1:09
@alev Perhaps you should email him and ask. – Alexander Gruber Feb 19 '13 at 1:10

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