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

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broilerc
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An analyst will recommend a combination of 3 industrial stocks.. [#permalink] New post  05 May 2016, 08:23
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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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Bunuel
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Re: An analyst will recommend a combination of 3 industrial stocks.. [#permalink] New post  05 May 2016, 08:31
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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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bazu
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An analyst will recommend a combination of 3 industrial stocks.. [#permalink] New post  25 Feb 2017, 09:36
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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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anasmousa
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Re: An analyst will recommend a combination of 3 industrial stocks.. [#permalink] New post  06 Dec 2017, 15:04
Why you are product them rather than add them ?

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Bunuel
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Re: An analyst will recommend a combination of 3 industrial stocks.. [#permalink] New post  06 Dec 2017, 20:51
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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] New post  08 Dec 2017, 12:55
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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.. [#permalink] New post  06 Jun 2022, 04:23
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Bunuel, GMAT Prep Question. Please tag it.
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Re: An analyst will recommend a combination of 3 industrial stocks.. [#permalink] New post  06 Jun 2022, 04:26
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AnkurGMAT20 wrote:
Bunuel, GMAT Prep Question. Please tag it.


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Re: An analyst will recommend a combination of 3 industrial stocks.. [#permalink] New post  06 Jun 2022, 12:37
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The analyst has to choose 3 industrial socks from 5; the number of ways to do this = \(5_C_3\) = 10

The analyst has to choose 2 transportation socks from 4; the number of ways to do this = \(4_C_2\) = 6

Finally, the analyst has to choose 2 utility socks from 3; the number of ways in which this can be done = \(3_C_2\) = 3

Total possible number of combinations of 7 socks = 10 * 6 * 3 = 180.
The correct answer option is D.
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Re: An analyst will recommend a combination of 3 industrial stocks.. [#permalink]
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