probability There are 5 cats 6 dogs and 3 goats boarded at t

There are 5 cats, 6 dogs, and 3 goats boarded at the kennel. If the vet\'s assistant walks 4 animals in the morning and if she chooses the animals at random, what is the chance that at least one animal of each of the three kinds are picked?

Solution

He has 14 animals, so there are 14C4 ways to choose any 4.

Now, we choose one each kind first. Then, there are 5*6*3 = 90 ways to do this. Then, we can choose the last one in 11 remaining ways. Thus, 90*11 = 990 ways.

Thus,

P(at least one of each kind) = 990 / (14C4) = 0.989010989 [ANSWER]