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Permutation and Combination problem

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by april24 » Fri Oct 16, 2015 6:19 am
Szechuan House offers chicken, shrimp, beef, vegetable, and tofu entrees served in either garlic sauce or green chili sauce.
In how many ways can three entrees be served if no entree is served more than a total of once?
A.10
B.60
C.80
D.100
E.120
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by GMATGuruNY » Fri Oct 16, 2015 6:27 am
april24 wrote:Szechuan House offers chicken, shrimp, beef, vegetable, and tofu entrees served in either garlic sauce or green chili sauce.
In how many ways can three entrees be served if no entree is served more than a total of once?
A.10
B.60
C.80
D.100
E.120
From the 5 entrees, the number of ways to choose 3 = 5C3 = (5*4*3)/(3*2*1) = 10.
Number of sauce options for the 1st entree = 2. (Garlic or green)
Number of sauce options for the 2nd entree = 2. (Garlic or green)
Number of sauce options for the 3rd entree = 2. (Garlic or green)
To combine the options above, we multiply:
10*2*2*2 = 80.

The correct answer is C.
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by Brent@GMATPrepNow » Fri Oct 16, 2015 6:41 am
Szechuan House offers chicken, shrimp, beef, vegetable, and tofu entrees served in either garlic sauce or green chili sauce. In how many ways can three entrees be served if no entree is served more than a total of once?

A)10
B)60
C)80
D)100
E)120

OAC
Take the task of serving 3 entrees and break it into stages.

Stage 1: Choose 3 meal types
There are 5 meal types: chicken, shrimp, beef, vegetable, and tofu
Since the order in which we select 3 meal types does not matter, we can use COMBINATIONS
We can select 3 meals from 5 meals in 5C3 ways (= 10 ways).
So, we can complete stage 1 in 10 ways

If anyone is interested, we have a free video on calculating combinations (like 5C3) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

Stage 2: Choose either garlic sauce or green chili sauce for the 1st selected meal.
We can complete this stage in 2 ways.

Stage 3: Choose either garlic sauce or green chili sauce for the 2nd selected meal.
We can complete this stage in 2 ways.

Stage 4: Choose either garlic sauce or green chili sauce for the 3rd selected meal.
We can complete this stage in 2 ways.

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus serve 3 entrees) in (10)(2)(2)(2) ways ([spoiler]= 80 ways[/spoiler])

Answer: C
--------------------------

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
- https://www.beatthegmat.com/mouse-pellets-t274303.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/ps-counting-t273659.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/please-solve ... 71499.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/laniera-s-co ... 15764.html

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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