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Megan Grywalski

Problem Set 4 9 . In how many ways can the number 14 be written as the sum of 5 nonnegative integers? In how many ways can 14 be written as the sum of 5 positive integers?. Megan Grywalski. In how many ways can the number 14 be written as the sum of 5 nonnegative integers?.

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Megan Grywalski

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  1. Problem Set 49. In how many ways can the number 14 be written as the sum of 5 nonnegative integers? In how many ways can 14 be written as the sum of 5 positive integers? Megan Grywalski

  2. In how many ways can the number 14 be written as the sum of 5 nonnegative integers? • Think of each expression broken down into a sum of 1’s (i.e. 5+3+2+0+4=14 =11111+111+11++1111=14) To find the number of ways to arrange 14 1’s and 4 +’s we would use: =

  3. Given an expression of nonnegative integers that sums to n, with m = number of integers you are adding and p=m-1 (p=+’s) we can use the formula to find the number of ways to sum m integers equal to n.

  4. In how many ways can 14 be written as the sum of 5 positive integers? • If we have a+b+c+d+e= 14 where a, b, c, d, and e are positive integers, we can change this to a sum of nonnegative integers by subtracting 1 from each a-1+b-1+c-1+d-1+e-1=14-5 a-1+b-1+c-1+d-1+e-1=9 Now we can use the same formula:

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