Ten days of statistics (4) - Combinatorics

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Permutations

A permutation is an ordered arrangement of $r$ objects from a set of $n$ items ( $0< r \leq n$ )

_nP_r = \frac{n!}{(n-r)!}

Note: We define $0! = 1$

Combinations

A combination is an unordered arrangement of $r$ objects from a set of $n$ items ( $0< r \leq n$ ) Intuitively we can calculate combination from permutation

_nC_r = \frac{_nP_r}{r!} = \frac{n!}{r! \times (n-r)!}

Example of permutation and combination

A school need to pick 11 players to form a team out of 100 candidates. This is a combination, there are $C \binom{100}{11}$ ways to form the team
A contest has 100 contestants and 3 medals (gold, silver, bronze) for 3 best performers. This is a permutation, there are $P \binom{100}{3}$ ways for the contest to end

Next lesson: Binomial distribution