Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $\{1,2,3,4,5\} = 5 \cdot 5 \cdot 5 \cdot 5$?

share|improve this question
1  
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

1 Answer 1

$(a)$ 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.

share|improve this answer
    
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
1  
@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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.