Admin: Created page with "Category:Statistics '''Counting''' is the concepts relating to the total possible number (i.e. count) of ways to do something given a certain population. The common forms include combination and permutation. = The Fundamental Principle = The '''fundamental principle''' of counting states that given k operations are performed, if there are $n_i$ ways to perform the i-th operation, then the ''total number of ways'' to perform the sequence of k operations is..."

2024-03-19T06:04:00Z

Created page with "Category:Statistics '''Counting''' is the concepts relating to the total possible number (i.e. count) of ways to do something given a certain population. The common forms include combination and permutation. = The Fundamental Principle = The '''fundamental principle''' of counting states that given k operations are performed, if there are <math>n_i</math> ways to perform the i-th operation, then the ''total number of ways'' to perform the sequence of k operations is..."

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[[Category:Statistics]]
'''Counting''' is the concepts relating to the total possible number (i.e. count) of ways to do something given a certain population. The common forms include combination and permutation.

= The Fundamental Principle =
The '''fundamental principle''' of counting states that given k operations are performed, if there are <math>n_i</math> ways to perform the i-th operation, then the ''total number of ways'' to perform the sequence of k operations is the product of all n. This makes sense so I'm not gonna elaborate.

= Permutation =
A '''permutation''' of a population is an ordering of a collection of objects. We calculate this with <math>n!</math>, and it makes sense so I'm not gonna elaborate.

= Combinations =
A '''combination''' of a population is a unique subset of it (i.e. a distinct group of objects). Notably different from permutations, the order does not matter.

The calculation is a bit complicated. Given <math>n</math> items and <math>k</math> items to insert, the total number of ways to select it can be calculated by the following:

<math>\left(^n_k \right) = \frac{n!}{(n - k)! k!}</math>

'''Quick derivation:''' the numerator is the number of possible permutations, and the denominator is the number of ways to arrange a permutation. Since order don't matter, we remove the permutations with different ordering but the same observations.

For all this, just use a calculator.

Counting - Revision history