Awareness Posted April 26, 2013 Share Posted April 26, 2013 Let's say I want to group numbers between 1 and 50 with 4 columns: 1 2 3 41 2 3 51 2 3 6...2 3 4 52 3 4 6...47 48 49 50 To find the total possible combinations,we do:50*49*48*47__________1*2*3*4This formula gives the maximum possible combinations. My question is,what would the formula be to find maximum of how many combinations ofthese numbers include number 1 and 2(for example)? Link to comment Share on other sites More sharing options...
John Posted April 27, 2013 Share Posted April 27, 2013 You would fix the specific numbers in the first however many slots and then work out the number of combinations for the remaining slots. In your initial example of finding all groups, you're calculating [math]50\choose4[/math] to find the number of possible combinations of four integers between 1 and 50 inclusive. If you wanted to find all combinations containing 1 and 2, then you would assume 1 and 2 occupy two slots, and then calculate how many ways to choose two numbers from the remaining 48 possibilities, i.e. you'd calculate [math]{{48}\choose{2}} = \frac{48!}{2!(48-2)!} = \frac{48\times47}{2}[/math]. Link to comment Share on other sites More sharing options...
Awareness Posted April 28, 2013 Author Share Posted April 28, 2013 Thank you,it works! Link to comment Share on other sites More sharing options...
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