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

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

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Re: An analyst will recommend a combination of 3 industrial stocks.. [#permalink]
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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]
AnkurGMAT20 wrote:
Bunuel, GMAT Prep Question. Please tag it.

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

5C3*4C2*3C2=180

If this would have been a question with repetition/twisted language this would have been an exciting one!
Re: An analyst will recommend a combination of 3 industrial stocks.. [#permalink]
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