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# a GWD math (8) , which hasn't been discussed

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a GWD math (8) , which hasn't been discussed [#permalink]  20 Aug 2011, 06:01
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Question Stats:

75% (02:09) correct 25% (02:43) wrong based on 0 sessions
There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. How many possible selections of 4 books from this shelf include at least one paperback?

a) 40
b) 45
c) 50
d) 55
e) 60
[Reveal] Spoiler: OA
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Re: a GWD math (8) , which hasn't been discussed [#permalink]  20 Aug 2011, 09:02
This can be solved by subtracting the no. of combinations that have all hardbacks from the total possible combinations

Total no. of ways to choose 4 books= 8C4
Total no. of ways to choose 4 books, which are hardbacks= 6C4

Hence, required number of books= 8C4-6C4= 70-15=55

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Re: a GWD math (8) , which hasn't been discussed [#permalink]  20 Aug 2011, 11:27
approach 1

at-least 1 paper back = total - no paper back
8c4-6c4 = 55

approach 2

at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back

= 2c1*6c3+2c2*6c2 = 55

Re: a GWD math (8) , which hasn't been discussed   [#permalink] 20 Aug 2011, 11:27
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