prob_all_choices.py

import random

attempts = 20000
choices = 25

def one_test(possibilities):
    found = []
    num = 0
    while len(found) < possibilities:
        r = random.randint(1,possibilities)
        if r not in found:
            found.append(r)
        num += 1
    return num

results = []
for i in range(attempts):
    results.append(one_test(choices))

print("Average over {} runs: {}".format(attempts, sum(results)/attempts))