Combinations refers to the grouping of items, sometimes this will allow repetition of objects while some will not. For example, you have 4 objects: A, B, C, and D. If you want to use all in your data set you will have 1 unique combination set where there is no repetition (ABCD) and then 35 combinations when repetition is allowed (ABCD, ABDC, ADBC, DABC, etc.).
A combination will be a general grouping of items without care to the order. With a permutation, order is important, each different ordering of items is a permutation. An example would be you have 5 fruits, how many combinations of all of these fruits can you make? 5, since you can only have all of these fruits once. In terms of permutations, you can rearrange these 5 fruits many different ways, 126, to be exact.
You should use combinations over permutations when the order of the selected items does not matter.
No, you can never have negative combinations of something since you are always choosing from a set of items where the number is positive.
Combinations relate to binomial coefficients because they number of combinations is often referred to as exactly that. It is the coefficient of the r-th term in the expansion of (x + y)n.
Create Date: September 25, 2024
Last Modified Date: October 5, 2024
