Answer to Question #139080 in Statistics and Probability for qwerty

Question

3. If 3 books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that
a. all books selected are novels?
b. 2 novels and 1 book of poems are selected?

Answer 1

There are 9 books on the shelf. We can pick up 3 book in

$\displaystyle C(9,3) = \frac{9!}{3!6!} = \frac{7 \cdot 8 \cdot 9}{3 \cdot 2}=84$ ways.

a) We can pick up 3 novels out 5 available in

$\displaystyle C(5,3) = \frac{5!}{3!2!} = \frac{5 \cdot 4}{2}=10$

So, the probability of "all books selected are novels" is

$P(A) = \frac{10}{84}= \frac{5}{42}$

b) We can pick up 2 novels and 1 book of poems in

$\displaystyle C(5,2) \cdot C(3,1) = \frac{5!}{2!3!} \cdot \frac{3!}{2!1!}= 10 \cdot 3=30$

The probability of event "2 novels and 1 book of poems are selected" is

$P(A) = \frac{30}{84}= \frac{5}{14}$

Answer: a) 5/42, b) 5/14