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An analyst will recommend a combination of

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by NandishSS » Sun Dec 18, 2016 6:10 am
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

OA:D

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by GMATGuruNY » Sun Dec 18, 2016 6:26 am
NandishSS 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
From 5 industrial stocks, the number of ways to choose 3 = 5C3 = (5*4*3)/(3*2*1) = 10.
From 4 transportation stocks, the number of ways to choose 2 = 4C2 = (4*3)/(2*1) = 6.
From 3 utility stocks, the number of ways to choose 2 = 3C2 = (3*2)/(2*1) = 3.
To combine these options, we multiply:
10*6*3 = 180.

The correct answer is D.
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by [email protected] » Sun Dec 18, 2016 10:56 am
Hi NandishSS,

In these types of multi-combination questions, you normally just have to find the individual number of combinations for each element, then multiply the results together.

From the information provided, the number of combinations of...

Industrial stocks = 5C3 = 10 possible combinations
Transportation stocks = 4C2 = 6 possible combinations
Utility stocks = 3C2 = 3 possible combinations

(10)(6)(3) = 180 possible combinations of 7 stocks.

Final Answer: D

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by Jay@ManhattanReview » Mon Dec 19, 2016 2:01 am
NandishSS 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

OA:D

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From the given 5 industrial stocks, the number of ways to choose 3 industrial stocks = 5C3 = 5C2 = (5*4)/(2*1) = 10.

We know that nCr = nC(n-r); if r > n/2, you must use this equivalent to ease the caculation. Remeber that nPr not equal to nP(n-r)

From 4 transportation stocks, the number of ways to choose 2 transportation stocks = 4C2 = 4C2 = (4*3)/(2*1) = 6.

From 3 utility stocks, the number of ways to choose 2 utility stocks = 3C2 = 3C1 = 3.

Number of different combinations of 7 stocks = 10*6*3 = 180.

OA: D.

-Jay

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by Scott@TargetTestPrep » Wed Dec 21, 2016 8:55 am
NandishSS 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

OA:D
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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