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An analyst will recommend a combination of 3 industrial stocks..

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An analyst will recommend a combination of 3 industrial stocks..  [#permalink]

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New post 05 May 2016, 07:23
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An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?

A. 12
B. 19
C. 60
D. 180
E. 720

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Posts: 50623
Re: An analyst will recommend a combination of 3 industrial stocks..  [#permalink]

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New post 05 May 2016, 07:31
1
2
broilerc wrote:
An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?

A. 12
B. 19
C. 60
D. 180
E. 720

--


5C3 * 4C2 * 3C2 = 10*6*3 = 180.

Answer: D.
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An analyst will recommend a combination of 3 industrial stocks..  [#permalink]

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New post 25 Feb 2017, 08:36
Bunuel wrote:
broilerc wrote:
An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?

A. 12
B. 19
C. 60
D. 180
E. 720

--


5C3 * 4C2 * 3C2 = 10*6*3 = 180.

Answer: D.



Hi Bunuel, when I faced this question I was a bit concerned by the fact that I am not dividing the 180 by 3!. In this way am I not considering the order why the order shouldn't be considered?

Thanks
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Re: An analyst will recommend a combination of 3 industrial stocks..  [#permalink]

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New post 06 Dec 2017, 14:04
Why you are product them rather than add them ?

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Re: An analyst will recommend a combination of 3 industrial stocks..  [#permalink]

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New post 06 Dec 2017, 19:51
anasmousa wrote:
Why you are product them rather than add them ?

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Because of Principle of Multiplication.

Principle of Multiplication
If an operation can be performed in ‘m’ ways and when it has been performed in any of these ways, a second operation that can be performed in ‘n’ ways then these two operations can be performed one after the other in ‘m*n’ ways.

21. Combinatorics/Counting Methods



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Re: An analyst will recommend a combination of 3 industrial stocks..  [#permalink]

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New post 08 Dec 2017, 11:55
1
broilerc wrote:
An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?

A. 12
B. 19
C. 60
D. 180
E. 720


We have a basic combination problem in which an analyst has to select 3 industrial stocks from 5, 2 transportation stocks from 4, and 2 utility stocks from 3. Let’s determine the number of ways to select each type of stock.

3 industrial stocks from 5: 5C3 = (5 x 4 x 3)/3! = (5 x 4 x 3)/(3 x 2 x 1) = 10 ways

2 transportation stocks from 4: 4C2 = (4 x 3)/2! = (4 x 3)/(2 x 1) = 6 ways

2 utility stocks from 3: 3C2 = (3 x 2)/2! = (3 x 2)/(2 x 1) = 3 ways

Since the analyst is choosing all 3 types of stocks, there are 10 x 6 x 3 = 180 ways to select the stocks.

Answer: D
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Re: An analyst will recommend a combination of 3 industrial stocks.. &nbs [#permalink] 08 Dec 2017, 11:55
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