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10 drinks are available. 6 of them are Pepsi Coke and 4 of

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10 drinks are available. 6 of them are Pepsi Coke and 4 of [#permalink] New post 07 Aug 2003, 18:43
10 drinks are available. 6 of them are Pepsi Coke and 4 of them Mountain Dew. You are picking 5 drinks, and least one drink is Moutain Dew. How many ways can you do this?
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 [#permalink] New post 07 Aug 2003, 18:55
5C1+5C2+5C3+5C4=30. Right?
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Re: Combination [#permalink] New post 07 Aug 2003, 22:29
boarderlee wrote:
10 drinks are available. 6 of them are Pepsi Coke and 4 of them Mountain Dew. You are picking 5 drinks, and least one drink is Moutain Dew. How many ways can you do this?


This is easy:

PC - Pepsi Coke
MD - Mountain Dew

Direct method:
1. Total # of combi of 5 drinks out of 16= 16C5
2. Total # of combi of no MD (all P) = 6C5
3. 1-2 and urdone.
--------------------------------

Indirect method:
1. 4C1*6C4 = Combi of one MD and 4 PC
2. 4C2*6C3 = Combi of two MD and 3 PC
3. 4C3*6C2 = Combi of tree MD and 2 PC
4. 4C4*6C1 = Combi of tree MD and 1 PC
5. 1+2+3+4 = must equal to step 3 in the direct method.

Somebody wants to check?
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Re: Combination [#permalink] New post 08 Aug 2003, 00:32
Konstantin Lynov wrote:
boarderlee wrote:
10 drinks are available. 6 of them are Pepsi Coke and 4 of them Mountain Dew. You are picking 5 drinks, and least one drink is Moutain Dew. How many ways can you do this?


This is easy:

PC - Pepsi Coke
MD - Mountain Dew

Direct method:
1. Total # of combi of 5 drinks out of 16= 16C5
2. Total # of combi of no MD (all P) = 6C5
3. 1-2 and urdone.
--------------------------------

Indirect method:
1. 4C1*6C4 = Combi of one MD and 4 PC
2. 4C2*6C3 = Combi of two MD and 3 PC
3. 4C3*6C2 = Combi of tree MD and 2 PC
4. 4C4*6C1 = Combi of tree MD and 1 PC
5. 1+2+3+4 = must equal to step 3 in the direct method.

Somebody wants to check?


There was a typing mistake if my explanation of direct method. Off course, there total # of combinations of 5 drinks is not out of 16, but out of ten.
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KL

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 [#permalink] New post 08 Aug 2003, 01:03
I agree with the expert, Stolyar: 10C5-6C5.

We don't have to worry about Mountain Dew because there are only 4 of them. Out of 5, one of them has to be Pepsi Coke.

Thanks.
  [#permalink] 08 Aug 2003, 01:03
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