A permutation refers to a combination of numbers in which the
order matters! Definition
n!= n x (n-1) x (n-2).. x 1
For exampleWe have 8 people:1: Alice2: Bob3: Charlie4: David5:
Eve6: Frank7: George8: Horatio How many ways can we award a 1st,
2nd and 3rd placeprize among eight contestants? (Gold / Silver /
Bronze)
(everyone take a moment to consider how to attempt this
question)
If we use permutations
Gold medal: 8 choices: A B C D E F G H One person wins Gold (can
be anyone)
Silver medal: 7 choices: B C D E F G H. One more person wins
Silver
Bronze medal: 6 choices: C D E F G H. Someone wins the
bronze.
We had 8 choices at first, then 7, then 6. The total number of
options was 8 x 7 x 6 = 336.
So this can be expressed in as 8!/5!Because 8x7x6 =
(8x7x6x5x4x3x2x1)/(5x4x3x2x1)
