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Counting Problem Consider the equation x+y+z+w=n, where n is a positive integer greater or equal to 4. A positive and integer solution is a set (x,y,z,w) of positive integers that satisfies the equation for a given n. For example, for n=10 one solution to x+y+z+w=10 would be (1,2,3,4), since 1+2+3+4=10. a) Determine the number of positive and integer solutions for n=10. b) Find a general formula that counts the number of whole and integer solutions for x+y+z+w=n. Note: Solutions (2, 2, 2, 4), (2, 2, 4, 2),(2, 4, 2, 2) and (4, 2, 2, 2) for n=10 are each considered different and separate solutions. |
Re: Counting Problem so. its finding the no of partitions of n as 4 integers.. it can be split like partitions of n as sum of two numbers.. and finding the partitions of those 2 numbers as sum of two numbers... |
Re: Counting Problem this can be proved by multinomial theorem... For a+b+c+d = n, the no. of solutions including 0 is need to eliminate those terms in the expansion of |
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Re: Counting Problem The number of co-efficients in the expansion of So for |
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((n-3)(n-2)(n-1))/6 I'm completely clueless as to the reasoning behind it, though, and politely ask for a baby explanation lol. |
Re: Counting Problem Hello, Jakarta! Quote:
Place 10 objects in a row, inserting a space between them. [color=beige]. . [/color] Select 3 of the 9 spaces and insert "dividers". Quote:
Following the solution in part (a), place Select 3 of the |
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Following the solution in part (a), place Select 3 of the [/quote:3oncju6n] Wow, that is extremely smart and clear. Thanks! |
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