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) The dictionary is selected?
b) 2 novels and 1 book of poems are selected? �
a) The probability of selecting the dictionary is 1/9. This is because there is only 1 dictionary out of a total of 9 books (5 novels + 3 books of poems + 1 dictionary).
b) The probability of selecting 2 novels and 1 book of poems is (5 choose 2) * (3 choose 1) / (9 choose 3).
The number of ways to select 2 novels from 5 is (5 choose 2) = 10,
the number of ways to select 1 book of poems from 3 is (3 choose 1) = 3,
the number of ways to select 3 books from 9 is (9 choose 3) = 84.
So, the probability is (10 * 3) / 84 = 30/84 = 5/14.