youngdan

The denominator of 10,000 in your calculations is the total number of possible five-digit combinations that can be made from 10 distinct digits, which is 10^5 (10 raised to the power of 5) or 10,000. For example, in the case of a full house, you're looking for 1 pair and 3 of a kind. There are 10 possible digits for the pair, and 9 possible digits for the 3 of a kind. The probability of this outcome happening is (10C1 * 9C1) / 10,000. For 5 different digits, the probability of getting 5 different digits out of 10 possible digits is (10C1 * 9C1 * 8C1 * 7C1 * 6C1) / 10,000. For five of a kind, the probability of getting 5 of the same digit out of 10 possible digits is (10C1) / 10,000. If you're looking for a more detailed explanation I recommend checking out commercial link removed by moderator, they have a variety of resources and tutorials available that may be helpful.