probability question

Question

A car rental agency has 11 midsized and 11 compact cars on its lot, from which 6 will be selected. Assuming that each car is equally likely to be selected and the cars are selected at random, determine the probability that the cars selected consist of all midsized cars.
What is the probability that the cars selected consist of all midsized cars?

Answer 1

There are 22 cars altogether.

The chances of the first car being midsized is 11 out of 22, or 1/2

Now there are only 21 cars,  The odds for the next one is 10 out of 21.

 

The number of midsized cars and total cars gets smaller by 1 after each selection.  The final odds will be:

P = (11/22) (10/21) (9/20) (8/19) (7/18) (6/17)

P = (11 x 10 x 9 x 8 x 7 x 6) / (22 x 21 x 20 x 19 x 18 x 17)

 

The shorthand way to write this is:

P = (11! x 16!) / (5! x 22!) ≈ 0.0062