For dinner at a restaurant, there are x choices of appetizers, y + 1

Question

For dinner at a restaurant, there are x choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?

A. x + y + z + 1
B. xyz + xz
C. xy + z + 1
D. xyz + 1
E. xyz + 1/2

A. x + y + z + 1
B. xyz + xz
C. xy + z + 1
D. xyz + 1
E. xyz + 1/2

BrentGMATPrepNow · Accepted Answer

Take the task of " building of a meal" and break it into   stages  .

Stage 1 : Select an appetizer
Since there are x choices, we can complete stage 1 in  x  ways

Stage 2 : Select a main course
Since there are y+1 choices, we can complete stage 2 in  y+1  ways

Stage 3 : Select a dessert
Since there are z choices, we can complete stage 3 in  z  ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and build the meal) in  (x)(y+1)(z)  ways (= xyz + xz ways)

Answer: B

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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OptimusPrepJanielle · Answer

x appetizers, 
y + 1 main courses, 
z dessert

Required: 1 appetizer, 1 main course, and 1 dessert
Number of ways possible = xC1*(y+1)C1*zC1 {NC1 = N! / (N-1)!*1! = N}

Hence, number of ways = x(y+1)z = xyz + xz

Correct Option: B

DigitsnLetters · Answer

We have to choose 1 appetizer, 1 main course, and 1 dessert for the meal out of x choices of appetizers, y + 1 main courses, and z choices of dessert.

This can be done in xC1 . (y+1)C1 . zC1 ways = x(y+1)z = xyz + xz (Option B).

Divyadisha · Answer

Possible ways to choose 1 appetizer out of x= x
Possible ways to choose 1 main course out of y+1= y+1
Possible ways to choose 1 dessert out of z= z

So possible ways to choose 1 appetizer, 1 main course, and 1 dessert:-

x (y+1) (z) = xyz+xz

B is the answer

Archit3110 · Answer

Let X,y,z each be 2 
Y;3 and X,z are both 2
Total choices of ordering one of each 2*3*2;12
Put value in option
Only b matches with 12 as (2*2*2+2*2)

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ckavishwar · Answer

Choose 1 appetizer, 1 main course, and 1 dessert for the meal out of x choices of appetizers, y + 1 main courses, and z choices of dessert.

=> xC1 . (y+1)C1 . zC1 ways = x(y+1)z = xyz + xz

Hence B

bumpbot · Answer

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For dinner at a restaurant, there are x choices of appetizers, y + 1

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