Combinatorics Tools for RMO

(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 

                         \(n!\)