Permutation subset

• Choose ordered subset k of n distinct objects

• Example: choose just 3 of 7 distinct objects

• 7 first choices, 6 second, 5 third

• n * ( n - 1 ) * [...] * ( n - k + 1 )

• Example: 7 * ( 7 - 1 ) * ( 7 - 3 + 1 ) = 7 * 6 * 5

• Same as dividing n factorial by ( n - k ) factorial: n * ( n - 1 ) * [...] * ( n - k + 1 ) * ( n - k ) * [...] * 1 -------------------------------------------------------------- ( n - k ) * [...] * 1

• n! / ( n - k )!

• Example: 7! / ( 7 - 3 )! = 7! / 4! = 7 * 6 *5