math - 使用排列组合的智商问题

Question

使用数字 54730 的所有数字，可以创建多少个小于 70000 和 5 的倍数的不同 5 位数字？

Answer 1

你会加起来：

5xxx0 = 3! = 6 combinations that start with 5 and end with 0
4xxx0 = 3! = 6 combinations that start with 4 and end with 0
4xxx5 = 3! = 6 combinations that start with 4 and end with 5
3xxx0 = 3! = 6 combinations that start with 3 and end with 0
3xxx5 = 3! = 6 combinations that start with 3 and end with 5

6*5 = 30 total combinations

注意：你不会做 7xxx0 或 7xxx5 因为它们会大于 70000

来源： https ://en.wikipedia.org/wiki/Combination#Number_of_k-combinations_for_all_k