Combination
A combination is a selection of elements in which the order of selection does not matter.
Statistics Every Programmer Needs
A combination is a selection of items in which order does not matter.
- How it is used
- Uses order-independent selection to structure counting and probability calculations.
- How deep it goes
- Explains order, replacement conditions, formulas, Pascal’s triangle, and Python implementations through worked small examples.
- Examples
- Uses a basketball lineup, Pascal’s triangle, and Python calculations with n = 5 and r = 3.
- What you can do after
- Apply it via Python’s math module to count order-independent selections with or without replacement.
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Fabulous Adventures in Data Structures and Algorithms
A combination is a subsequence or subset selected from a sequence without changing the original element order.
- How it is used
- Uses combinations to generate cases where sequence items are skipped and to select items from arbitrary lists through their indices.
- How deep it goes
- Develops mutable and recursive enumeration, counting identities, an iterative Choose implementation, and direct retrieval by position.
- Examples
- Works through ABCDE with k = 3, selecting foods by index, and advancing the four-index combination 1245 to 0345.
- What you can do after
- Build it from scratch: enumerate combinations, count them with Choose, or retrieve one directly by its position.
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Statistics Slam Dunk
A combination is a selection of objects or values in which the order of the selected elements does not matter.
- How it is used
- Frames combinations as a classification step before counting possibilities or analyzing NBA scheduling data.
- How deep it goes
- Defines order-independent selection and contrasts it with permutations, but does not develop a combination-counting formula.
- Examples
- Uses a Warriors starting lineup, locker numbers, division standings, and NBA teams’ prior days off.
- What you can do after
- Evaluate whether a counting problem requires combinations or permutations before computing it in R.
Related concepts
- permutationcontrasts with · A permutation is a bijective rearrangement of the elements of a finite set, equivalently an ordering in which each element appears exactly once.
- binary stringalternative to · A binary string is a finite, ordered sequence of binary digits, each having the value zero or one.
- binomial coefficientequivalent to · A binomial coefficient is the number of ways to select a specified number of elements from a finite set, without regard to order.
- combination with replacementincludes · A combination with replacement is a selection in which order does not matter and selected items may be selected again.
- combination without replacementincludes · A combination without replacement is a selection in which order does not matter and selected items cannot be selected again.
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