MHB What Are the Odds of All Canadian NHL Teams Missing the Playoffs?

[A Rolfson]

I am a writer trying to calculate possible outcomes in sports - specifically, relating to the NHL:

There are 30 teams in the league, my questions are:

All else being equal (ie. random draw), what are the chances of all 7 Canadian NHL franchises finishing in the last fourteen -meaning they're out of the playoffs - in a given year?

What are the chances of all 7 of them finishing in the last ten?

Never took math/prob-stats beyond high school, so any help would be appreciated, including tips or a formula for calculating such things myself.

Thanks,

 

[squidsk]

First I'm going to assume that the order they finish in the last 14/10 doesn't matter.

To find out the probability you calculate the number of total number of different of teams finishing in the last 14 (whether or not they are Canadian) which is given by:

$${30 \choose 14}=145422675$$

Then figure out the number of combinations which have only the Canadian teams in the bottom 14:

$${7 \choose 7} * {23 \choose 7}= 1 * 245157 = 245157$$

Note: The first term is because you have to choose all 7 Canadian teams from the 7 in the league and the second terms is because you are choosing the remaining 7 teams from the remaining 23 teams.

Then divide the second number by the first to get your percentage:

$$245157 / 145422675 \approx 0.2\% $$

You do a similar calculation for the bottom 10:

$${30 \choose 10}=30045015$$

$${7 \choose 7} * {23 \choose 3}= 1 * 1771= 1771$$

$$1771 / 30045015 \approx 0.006\% $$