Binomial Coefficients and Generating Functions - Cs.ioc.ee

Example: 100 Euro
How many ways 100 Euro can be changed using smaller banknotes?
Generating functions for selecting banknotes of 5, 10, 20 or 50 Euros:
Generating function for the task
A(x) = x 0 + x 5 + x 10 + x 15 + ··· = 1
1 − x5 B(x) = x 0 + x 10 + x 20 + x 30 1
+ ··· =
1 − x10 C(x) = x 0 + x 20 + x 40 + x 60 1
+ ··· =
1 − x20 D(x) = x 0 + x 50 + x 100 + x 150 1
+ ··· =
1 − x50 P(x) = A(x)B(x)C(x)D(x) =
1
(1 − x 5 )(1 − x 10 )(1 − x 20 )(1 − x 50 )