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# On a shelf there are 6 hardback books and 2 paperback book.

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On a shelf there are 6 hardback books and 2 paperback book. [#permalink]
ferrarih wrote:
On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book?

A. 11/14
B. 5/7
C. 2/7
D. 3/14
E. 1/7

OA:A

The probability of picking up at least one paperback book $$= 1 -$$ The probability of picking up no paperback book $$= 1- \frac{C(6,4)}{C(8,4)}= 1-\frac{3}{14}=\frac{11}{14}$$
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Re: On a shelf there are 6 hardback books and 2 paperback book. [#permalink]
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ferrarih wrote:
On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book?

A. 11/14
B. 5/7
C. 2/7
D. 3/14
E. 1/7

The phrase “at least one paperback” means “one or more paperbacks.” Thus, the only way we would NOT pick up at least one paperback would be if all 4 books were hardbacks. Thus, we can use the formula:

P(at least one paperback) = 1 - P(all hardbacks)

The number of ways to select all hardbacks is 6C4:

6! / (4! x 2!) = (6 x 5) / (2 x 1) = 15

The number of ways to select 4 books from 8 is 8C4:

8! / (4! x 4!) = (8 x 7 x 6 x 5) / (4 x 3 x 2 x 1) = 7 x 2 x 5 = 70

The probability of all hardbacks is 15/70 = 3/14 and thus P(at least on paperback) = 1 - 3/14 = 11/14.

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Re: On a shelf there are 6 hardback books and 2 paperback book. [#permalink]
ferrarih wrote:
On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book?

A. 11/14
B. 5/7
C. 2/7
D. 3/14
E. 1/7

total possible ways = ( 1- ( 6/8* 5/7 * 4/6 * 3/5) ) = 11/14
IMO A
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Re: On a shelf there are 6 hardback books and 2 paperback book. [#permalink]
Hardback books = 6
Paperback books = 2
Total = 8

4 books picked at random: $$^8{C_4} =70$$

At least one paperback: 1 - all 4 hardback

4 hardback books picked out of 6: $$^6{C_4} = ^6{C_2} = 15$$

Probability: $$\frac{15}{70} = \frac{3}{14}$$

At least one paperback: $$1 - \frac{3}{14} = \frac{11}{14}$$

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Re: On a shelf there are 6 hardback books and 2 paperback book. [#permalink]
On a shelf there are 6 hardback books and 2 paperback book. If we pick up 4 books at random, what is the probability that we pick up at least one paperback book?

A. 11/14
B. 5/7
C. 2/7
D. 3/14
E. 1/7
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Re: On a shelf there are 6 hardback books and 2 paperback book. [#permalink]
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Re: On a shelf there are 6 hardback books and 2 paperback book. [#permalink]
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