In an animal shelter with 30 animals, each of which is either a cat or a dog, 12 out of 15 dogs have long fur and 11 out of 15 cats have long fur. What is the probability that in a randomly selected group of five animals from the shelter, there will be two long-furred dogs and three long-furred cats? Express your answer as a decimal to the nearest thousandth.

I got (5C2)*((12C2)+(11C3))/(30C5) but I'm not sure because that probability seems unreasonably low so it would be nice if anyone was willing to check. Thanks!

idontknowhowtodivide Feb 21, 2023

#2**+1 **

This is how I would look at it.

Choose 2 dogs from 12 long haired ones and Choose 3 cats from ll long haireds ones

and put it over 5 animals from a total of 30 animals

= ( 12C2 * 11C3 ) / 30C5 = 66*165 / 142506 = 10890 / 142506 = 605 / 7917 = approx 7.6%

That sounds ok to me.

I do not know why you multiplied that by 5C2

Melody Feb 22, 2023

#3**+1 **

5 choose 2 is the number of ways to pick the order of the ways you pick a dog and cat, but now I realize that's probably wrong.

idontknowhowtodivide
Feb 22, 2023

#4**+1 **

ok now I understand what you have done.

In this case order does not count. I am glad you worked that out for yourself :)

Melody
Feb 23, 2023