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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?



Answer :

Part a: The probability of selecting a dictionary is 1/3

Part b: The probability of selecting 2 novels and 1 poem book is 5/14

Number of novels = 5

Number of poem books = 3

Number of dictionary = 1

Total number of books = 9

Part a:

Number of ways to select 3 books from 9 books = C(9,3) = 84

Probability of selecting the dictionary = C(1,1) = 1

The other two books can be selected amongst any of the remaining 8 books, the probability = C(8,2) = 28

So, probability = 28*1/84 = 1/3

Part b:

Probability of selecting two novels = C(5,2) = 10

Probability of selecting 1 poem book = C(3,1) = 3

Probability = 10*3/84 = 5/14

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