Datasets:
| from itertools import permutations | |
| from fractions import Fraction | |
| valid, divisible, first_one = 0, 0, 0 | |
| for digits in permutations(range(6), 4): | |
| if digits[0] == 0: | |
| continue | |
| valid += 1 | |
| number = 1000 * digits[0] + 100 * digits[1] + 10 * digits[2] + digits[3] | |
| if number % 5 == 0: | |
| divisible += 1 | |
| first_one += digits[0] == 1 | |
| assert first_one == 24 | |
| result = {"total": valid, "divisible": divisible, | |
| "p_divisible": str(Fraction(divisible, valid)), | |
| "p_first_one_given_divisible": str(Fraction(first_one, divisible))} | |
| import json | |
| print(json.dumps(result, ensure_ascii=False, sort_keys=True)) | |