Subsets of CombinationsDate: 10/05/2003 at 19:38:19 From: Tyler Subject: Subsets How many subsets of size 10 of the numbers 1, 2, 3, ..., 20 have 5 as the smallest element? Date: 10/05/2003 at 20:23:14 From: Doctor Luis Subject: Re: Subsets Hi Tyler, There are C(20,10) = 20*19*18*...*10 / 10! = 184756 subsets with 10 elements because you are choosing 10 elements out of 20. Now, how many of these contain 5 as an element? If you choose 5, then the other 9 elements in your subset are chosen from 19 possibilities, hence there are C(19,9) = 92378 subsets which contain 5. However, 5 is supposed to be the smallest element. So, the numbers 1, 2, 3, and 4 are forbidden. In reality, you don't have 19 choices to fill those 9 extra spots in your subset. You have only 15 choices: 6, 7, ..., 19, 20 So, there are C(15,9) choices for the other 9 elements. How many would that be? I'll leave that for you to calculate :) Get it? I hope this helped! Let us know if you have any more questions. - Doctor Luis, The Math Forum http://mathforum.org/dr.math/ |
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