Binomial Exactly k Balls in a Bin

Problem

Balls are thrown independently and uniformly into bins bins. Return the probability a fixed bin receives exactly k of the balls:

P = C(balls, k) * (1 / bins)^k * (1 - 1 / bins)^(balls - k).

Return 0.0 for invalid arguments.

Hint

Condition on one bin; its load is Binomial(balls, 1 / bins).

case 1

in: [10,10,0]

expected: 0.3486784401000001

case 2

in: [2,2,1]

expected: 0.5

case 3

in: [3,6,0]

expected: 0.5787037037037038

case 4

in: [1,0,0]

expected: 0

Starter codePython

import math


def bin_exactly_k_balls(balls, bins, k):
    # Your code here
    pass

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