4909.sagews

n = var('n')

N = var('N')

l = var('l')

binomial(n,l)

binomial(n, l)

p = binomial(n, l) * ((1.0/N)**l) * (((N-1.0)/N)**(n-l))

p(n = 1600000000, N = 12500000, l = 5)

7.36500244325767e-48

sum(p(n = 1600000000, N = 12500000, l = x) for x in range(129))

0.523484483921707