§ Counting with repetitions via pure binomial coefficients
- If we want to place things where of them are of kind
a, are of kind
b, of them are kind . the usual formula is .
- An alternative way to count this is to think of it as first picking slots from , and then picking slots from the leftover elements, and finally picking slots from . This becomes .
- This is equal to , which is equal to the usual by cancelling and setting .
- Generalization is immediate.