Dr. J’s Guide to Combinations (without replacement)

Dr. J introduces combinations (without replacement) which is an unordered set of k elements taken from a set of n elements where elements cannot be repeated. He provides intuition behind the formula for combinations, which is n factorial divided by (n-k) factorial times k factorial. Namely, combinations (without replacement) are just permutations (without replacement) except without the k factorial permutations of the k items. Thus the formula is the formula for permutations (without replacement) divided by the number of permutations (without replacement) of k items. This formula is applied to find the number of possible starting hands for Texas Hold ‘Em and Euchre.