Python assignment.

1. Use product() to make a function which counts the number of ways you can place unlabeled balls in labeled urns given lower and upper bounds on how many balls each urn can have. Your function should take in four integers

n - number of balls

k - number of urns

lower - the smallest number of balls allowed in an urn

upper - the largest number of balls allowed in an urn

It should spit out a list of all the possible configurations.

bounded_urns(n,k,lower,upper)

>>> bounded_urns(13,4,2,4) [(2, 3, 4, 4), (2, 4, 3, 4), (2, 4, 4, 3), (3, 2, 4, 4), (3, 3, 3, 4), (3, 3, 4, 3), (3, 4, 2, 4), (3, 4, 3, 3), (3, 4, 4, 2), (4, 2, 3, 4), (4, 2, 4, 3), (4, 3, 2, 4), (4, 3, 3, 3), (4, 3, 4, 2), (4, 4, 2, 3), (4, 4, 3, 2)]

>>> bounded_urns(5,7,0,1) [(0, 0, 1, 1, 1, 1, 1), (0, 1, 0, 1, 1, 1, 1), (0, 1, 1, 0, 1, 1, 1), (0, 1, 1, 1, 0, 1, 1), (0, 1, 1, 1, 1, 0, 1), (0, 1, 1, 1, 1, 1, 0), (1, 0, 0, 1, 1, 1, 1), (1, 0, 1, 0, 1, 1, 1), (1, 0, 1, 1, 0, 1, 1), (1, 0, 1, 1, 1, 0, 1), (1, 0, 1, 1, 1, 1, 0), (1, 1, 0, 0, 1, 1, 1), (1, 1, 0, 1, 0, 1, 1), (1, 1, 0, 1, 1, 0, 1), (1, 1, 0, 1, 1, 1, 0), (1, 1, 1, 0, 0, 1, 1), (1, 1, 1, 0, 1, 0, 1), (1, 1, 1, 0, 1, 1, 0), (1, 1, 1, 1, 0, 0, 1), (1, 1, 1, 1, 0, 1, 0), (1, 1, 1, 1, 1, 0, 0)]

>>> len(bounded_urns(20,6,0,4))

126