"""
 365 days in the year
 N people in the room

 2 people: chances of same birthday:   1/365

 1 person in room:       can't collide
 2 person in the room    364/365                            p
 3 person in room        (363/365) * (364/365)              p
 4 person in room        (362/365) * (363/365) * (364/365)
"""

#   10*9*8
#
#   10*9*8*7*6*5*4*3*2*1         10! / (10-3)!
#          7*6*5*4*3*2*1


def birthday(n, m):
    """ probability of at least two overlaps 
        with n things out of m slots """
    # m = 365 is the birthday problem
    # product of (m-1)*(m-2)*(m-3)*..../m*m*m*...
    #            ---- n-1 terms ------  --- n-1 terms ------
    p = 1
    for i in range(1, n):
        p = p * (m-i)/m
    return 1 - p

for x in range(1, 30):
    print(f"birthday({x}) is {birthday(x,365)}.")