View source for User:Ryanbear

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==stars and bars on differences==
To find the number of ways to choose <math>n</math> numbers between <math>a</math> and <math>b</math> if they are indistinguishable but can have duplicates let <math>a_1</math> be the difference between the smallest number and <math>n</math>, <math>a_2</math> be the difference between the 2rd and 1st smallest numbers, and similar logic to get <math>a_{n+1}</math> is the difference between <math>b</math> and the largest number. <math>a_1+a_2+...+a_{n+1}=b-a</math>. Then use stars and bars to get <math>{n+b-a \choose n}</math>