Partial Coupon Collection Expected Draws

Problem

Expected number of draws needed to collect m distinct coupon types out of n equally likely types, summing the geometric waiting times n / (n - j) for j = 0 to m - 1. Return 0.0 for n <= 0, m < 0 or m > n.

Hint

With j distinct types already collected, the wait for a new one is geometric with success probability (n - j) / n.

Test cases

case 1

in: [6,6]

expected: 14.7

case 2

in: [10,1]

expected: 1

case 3

in: [5,3]

expected: 3.916666666666667

case 4

in: [4,0]

expected: 0

case 5

in: [3,4]

expected: 0

Starter codePython

def partial_coupon_collection_draws(n, m):
    # Your code here
    pass

5 test cases · run your code against them in the editor