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# A certain tin contains exacly 10 identically shaped

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Director
Joined: 29 Aug 2005
Posts: 769
A certain tin contains exacly 10 identically shaped  [#permalink]

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08 Apr 2007, 10:32
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

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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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Manager
Joined: 22 Feb 2007
Posts: 64

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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.
Manager
Joined: 28 Feb 2007
Posts: 186
Location: California

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08 Apr 2007, 11:06
1
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
Joined: 29 Aug 2005
Posts: 769

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08 Apr 2007, 11:57
OA C

Any other ways to solve this?
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4821
Location: Singapore

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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

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Non-Human User
Joined: 09 Sep 2013
Posts: 9162
Re: A certain tin contains exacly 10 identically shaped  [#permalink]

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15 Aug 2018, 11:19
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Re: A certain tin contains exacly 10 identically shaped &nbs [#permalink] 15 Aug 2018, 11:19
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