- #1

mr_coffee

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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~

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~

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