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A certain tin contains exacly 10 identically shaped

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Director
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A certain tin contains exacly 10 identically shaped [#permalink] New post 08 Apr 2007, 10:32
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A certain tin contains exacly 10 identically shaped gumdrops, of which 2 are cherry, 2 are lemon , 2 are grape, 2 are cinnamon and 2 are strawberry.
If 2 gumdrops are randomly selected, one at a time and without replacement, what is the probability that the second gumdrop is the same flavour as the first?
A 1/45
B 1/25
C 1/9
D 1/5
E 2/5
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 [#permalink] New post 08 Apr 2007, 10:57
1/9, as only one gumball of same flavor is present among the remaining nine after picking the 1st one.
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Re: PS: Probability [#permalink] New post 08 Apr 2007, 11:06
botirvoy wrote:
A certain tin contains exacly 10 identically shaped gumdrops, of which 2 are cherry, 2 are lemon , 2 are grape, 2 are cinnamon and 2 are strawberry.
If 2 gumdrops are randomly selected, one at a time and without replacement, what is the probability that the second gumdrop is the same flavour as the first?
A 1/45
B 1/25
C 1/9
D 1/5
E 2/5


P(chosing 1st one) = 1. Now P of same flavor remaining = 1/9 Hecen answer = 1/9

Another way of doing it
# ways to chose 2 from 10 = 10 C 2 = 45
# Ways to chose such that both are same = 5
Hence probability = 5/45 = 1/9
Director
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 [#permalink] New post 08 Apr 2007, 11:57
OA C

Any other ways to solve this?
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 [#permalink] New post 08 Apr 2007, 20:36
Here's a straight-forward way without all those combinatorics invovled.

Either get 2 cherry, 2 lemon, 2 grape, 2 cinnamon or 2 strawberry.

For each case, the probability = 1/10 * 1/9 = 1/90

For 5 cases, P = 5/45 = 1/9
  [#permalink] 08 Apr 2007, 20:36
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