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There are 8 books in a shelf that consist 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?

 Jan 30, 2020
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To get at least one paperback book:

Either two paperback books and four hadrback books:  2C2 · 6C4  =  15

Or one paperback book and five hardback books:         2C1 · 6C5  =  12

 

Since these are mutually exclusive, adding them together = 27 ways.

 Jan 30, 2020

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