balls.py

def choose(n, k):
    """
    A fast way to calculate binomial coefficients by Andrew Dalke (contrib).
    """
    if 0 <= k <= n:
        ntok = 1
        ktok = 1
        for t in xrange(1, min(k, n - k) + 1):
            ntok *= n
            ktok *= t
            n -= 1
        return ntok // ktok
    else:
        return 0

def a(N, P, n):
    res = 1
    for i in range(n):
        res *= (P-i)/float(N-i)
    return res

def f(N, W, B, K, T):
    res = choose(K, T) * a(N, W, T) * a(N-T,B,K-T)
    #res = choose(K, T) * (float(B)/N)**(K-T) * (float(W)/N)**(T)
    print(str(T) + " white balls: " + str(res))
    return res
N = 10
W = 3
B = 7
K = 7
print(sum([f(N, W, B,K, T) for T in range(0,4)]))