My Math Forum Complex Combinations Within Combinations Problem?

 January 22nd, 2011, 04:55 PM #1 Newbie   Joined: Jan 2011 Posts: 2 Thanks: 0 Complex Combinations Within Combinations Problem? Given are the possible combinations of 5 numbers from 1 - 35 (35c5= 324632 combinations), which are rearranged to build combinations of six numbers. Each of these 6-number-combinations contains 6c5=6 subsets of five #s. Thus, 324632/6= 54.105 are the combinations of 6 #s containing all the possible subsets of five #s. The question is how many of those 54.105 combinations contain the subset 1, 2, 3, 4, 5. PS. If we had all combinations of six #s (35c6) instead of 35c5 the obvious answer would be 30. How is it however with the new pattern (combinations of six #s built to contain the 324632 subsets of five #s, as described above)?
January 23rd, 2011, 02:41 PM   #2
Math Team

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Re: Complex Combinations Within Combinations Problem?

Hello, bugrocket!

I hope that wasn't the original wording of the problem.
[color=beige]. . [/color]It's awful! . . . clumsy, confusing, and misleading.

Quote:
 A subset of six numbers are chosen from the integers 1 to 35 (without replacement). How many of the possible subsets contain {1,2,3,4,5} ?

Note: We don't care how many possible subsets there are . . .

We are told that $\{1,\,2,\,3,\,4,\,5\}$ are already in the subset.

The sixth number can be any of the other 30 numbers.

Therefore, there are 30 subsets with $\{1,\,2,\,3,\,4,\,5\}.$

 January 23rd, 2011, 05:02 PM #3 Newbie   Joined: Jan 2011 Posts: 2 Thanks: 0 Re: Complex Combinations Within Combinations Problem? thanks! That was my first thought too! How many would there be however if we had all possible combinations of six numbers and we'd be looking for one containing a specific 5-number subset? Example. We have all possible combinations of six from 1-35 and we are looking for all those that contain the numbers 1,2,3,4,5. According to your solution it would again be 30. How is it possible?

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