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oryxncrake
Average Member
USA
7 Posts |
 Posted - 10/28/2009 : 19:57:10
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hi
can anyone help me on this question involving combinatorics?
as a party favor, each person invited to the party is given two bottles of wine. there is a total of 19 bottles of wine to choose from, 10 of which are red wine and 9 of which are white wine.
the question is: how many different party favors are possible if at least one of the two bottles of wine were white wine? |
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galactus
Advanced Member
USA
1460 Posts |
Posted - 10/29/2009 : 08:12:00
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There are two cases to consider. One red and one white or both white.
One red and one white: C(10,1)*C(9,1)
Both white: C(9,2)
Add them up: 90+C(9,2)
Also, we could find the number where this is no white and subtract from the total number of combinations of two bottles.
There is no white if they are both red.
C(10,2). The total number of ways is C(19,2)
C(19,2)-C(10,2)
Should be same answer for both methods.
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oryxncrake
Average Member
USA
7 Posts |
Posted - 10/29/2009 : 20:14:36
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THanks a lot!
quote:
Originally posted by galactus
There are two cases to consider. One red and one white or both white.
One red and one white: C(10,1)*C(9,1)
Both white: C(9,2)
Add them up: 90+C(9,2)
Also, we could find the number where this is no white and subtract from the total number of combinations of two bottles.
There is no white if they are both red.
C(10,2). The total number of ways is C(19,2)
C(19,2)-C(10,2)
Should be same answer for both methods.
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oryxncrake
Average Member
USA
7 Posts |
Posted - 10/29/2009 : 20:16:45
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| but how can i tell the difference when solving a problem between a permutation and combination? |
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galactus
Advanced Member
USA
1460 Posts |
Posted - 10/30/2009 : 14:10:10
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Order matters in permutations. It does not with a combination.
For instance, a common misnomer is 'combination lock'. When we open a so-called combination lock, the order of the numbers matters. That is actually a permutation, not a combination. |
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the_hill1962
Advanced Member
USA
1305 Posts |
Posted - 11/01/2009 : 19:08:16
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| galactus: Thanks for the "common misnomer". I never thought of it that way. |
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more perms and combinations!
