Probability of Fantasy Football Draft Order results?

Question

If you had 10 teams, and numbers were drawn from a hat, what is the probability that the 9 and 10th picks would go to the two people who were not actually at the draft? (I bet it 100% :) ) But does anyone know how to calculate this?

Answer 1

So, your saying there are 10 teams and only 8 of the 10 "managers" show up to draft day.  What are the odds that the 9th and 10th picks would be left for the two missing people (assuming everyone else picked from a hat that had the numbers 1 through 10 in it).

first person has a 8/10 chance of not picking 9 or 10

second person has a 7/9 chance

third person has a 6/8 chance and so on

P(not 9 or 10 for first 8 people) is 8/10 * 7/9 * 6/8 * 5/7 * 4/6 * 3/5 * 2/4 * 1/3 = 0.02222222....

as a percentage

2.2222222...%

Represented as a math equation the formula is

8! * 2! / 10!