Picking 3 random books probability problem

Question

So the question is: Suppose a bookcase holds 6 chemistry, 5 math, 3 physics, and 8 computer science texts. if 3 books are selected, find the probability that none of the math texts are selected.

My attempt at this question is since there are 22 books total, we can just subtract 5 from the total and get 17 so 17/22 is the probability. I do not believe this is right though because it just seems too easy. What am i doing wrong, if i am doing it wrong?

Answer 1

Some hints:

• What is the probability of not taking a math book?
• What is the probability of not taking a math book if one non-math book has been removed?
• What is the probability of not taking a math book if two non-math books have been removed?

The total probability is the product of these three probabilities.

Answer 2

6 Chemistry, 5 Math, 3 Physics, and 8 Computer books. Total 22 Books.

I looked at it using Hypergeometic Probability. $$P(X=x)={{N_1\choose x}{N_2\choose n-x}\over{N\choose n}}$$ Where our $N_1=5,N_2=17,N=22,n=3,x=0$ $$P(X=0)={{5\choose 0}{17\choose 3}\over{22\choose 3}}={4\over17}$$