# Month: June 2020

## 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 …

## Dr. J’s Guide to Permutations (without Replacement)

Permutations (without replacement) are an ordered set of k elements taken from a set of n elements where elements cannot be repeated. In constructing this set, we have n choices for the first element, (n-1) choices for the second element, and so on until we have (n-k+1) choices for the kth element. Thus the formula …

## Dr. J’s Guide to Permutations with Replacement

Dr. J introduces delves into more detail on permutations with replacement including intuition behind the formula and additional examples. To aid the intuition, the Fundamental Rule of Counting is introduced that states “if there are a ways of doing one thing and b ways of doing another thing, then there are a times b ways …

## Dr. J’s Guide to Counting

Dr. J introduces the four basic types of counting: combinations and permutations both with and without replacement. Combinations occur when order does not matter while permutations occur when order does matter. The video shows examples of using formulas to perform the counting for each the four basic types of counting.