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#specialist#ae#permutation#combinations

difference between permutation and combination §

permutation is arrangement of things

• order matters in permutations
• $ABC$ and $BCA$ are different permutations of letters A,B,C a combination is a collection of things
• order is irrelevant in combinations
• $ABC$ and $BCA$ are the same combination
• $ABC$ and $BCD$ are different combinations permutation formula for A, B, C and D
• $4\times 3\times 2\times 1=4!$
• the number of permutations of n objects is n! for all integers $n\ge 1$ $n\times (n-1)\times (n-2)\times \cdots \times 1$ and $0=1$

digression §

recursive definition:

• for all integers $n\ge 1$ $n!=n\times (n-1)!$
• and $0=1$
• simplifying expressions involving factorials. given m! and n! where m < n, the highest common factor is m!
• evaluate that shit

taken r at a time §

list all permutations of a b c d and e taken 2 at a time

general formula is $\frac{n!}{(n-r)!}$