sim.py

import random

RUNS = 10**3

APPLICANTS = 124000
ACCEPTED_1 = 20000
ACCEPTED_2 = 65000
FRIENDS = 4


def do_run():
    batch = range(APPLICANTS)
    random.shuffle(batch)
    while any(x < FRIENDS for x in batch[:ACCEPTED_1]):
        random.shuffle(batch)
    return sum(x < FRIENDS for x in batch[ACCEPTED_1:ACCEPTED_2])

if __name__ == '__main__':
    selected = [0] * (FRIENDS + 1)
    for run in xrange(RUNS):
        if run % 1000:
            print 'Done %s runs' % (run, )
        num_selected = do_run()
        selected[num_selected] += 1

    print 'After %s runs,' % (RUNS, )
    for i, n in enumerate(selected):
        print '%s people were selected %s times' % (i, n)