swerve wrote:There are 8 books in a shelf that consists of 2 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
A. 40
B. 45
C. 50
D. 55
E. 60
The OA is D.
Please, can anyone explain this PS question? I tried to solve it but I can't get the correct answer. I need help. Thanks.
Combinations with at least 1 paperback = (all possible combinations) - (combinations with no paperbacks).
All possible combinations:
From the 8 books, the number of ways to choose 4 = 8C4 = (8*7*6*5)/(4*3*2*1) = 70.
Combinations with no paperbacks:
From the 6 hardback books, the number of ways to choose 4 = 6C4 = (6*5*4*3)/(4*3*2*1) = 15.
Combinations with at least 1 paperback:
70-15 = 55.
The correct answer is
D.
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