# Combinatorics Tools for RMO

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## (Work in Progress)

1. The number of permutations  of $$n$$ objects taken $$r$$ at a time is

$$n(n-1)(n-2)(n-3) \cdot\cdot\cdot (n-r+1)$$.

2. The symbols

$$^nP_r ; P(n,r) ; n_r$$

are all used by mathematicians to denote the (above) number of permutations of $$n$$ things taken r at a time .

3. The number

$$n(n-1)(n-2)\cdot\cdot\cdot 3\cdot 2\cdot 1$$

is called ‘Factirial $$n$$ ‘ and denoted by

$$n!$$