By changing the order would it change the answer? r-combinations

[mr_coffee]

Hello everyone.

The book gave an example of the following problem:

#5. If n is a positve integer, how many 4-tuples of integers from 1 through n can be formed in which the elemnets of the 4-tuple are wirtten in increasing order but are not necessarily distinct? In other words, how many 4-tuples of integers (i, j, k, m) are there with 1 <= i <= j <= k <= m <= n?

Using the following formula:
The number of r-combinations with repetition allowed (multisets of size r) that can be selected form a set of n elements is

(r + n -1)
( r )

This equals the number of ways r objects can be selected from n categories of objects with reptition allowed.


The answer is on the following image marked #5.

http://suprfile.com/src/1/411mnhi/lastscan.jpg


The problem I'm doing is marked #6. The only difference in the problem is now they want to know how many 5-tuples of integers from 1 through n, wirtten in DECREASING order. In other words, how many 5-tuples of integers (h, i, j, k, m) are there with n >= h >= i >= j >= k >= m >= 1?

I would assume it would be the same format, let r = 5 instead of 4 is the only change I would think would be made. Because I thought order doesn't matter, so even if they say accessending or decending would it change the formula?

Thanks~

 

[mattmns]

No, the order should not change the answer.

Think about it like this. If you go back to problem number 5, and now flip the order around (meaning that you take every (i,j,k,l) and change it into (l,k,j,i) you will then have decreasing numbers, but you will have the exact same amount since you are not really doing anything but looking at the same thing backwards.

 

[mr_coffee]

THanks for the help matt!