A pizza can be assembled from given choices, with customer’s preferenc

Question

A pizza can be assembled from given choices, with customers' preferences. The crust is available in 3 varieties – cheese burst, classic, and wheat thin; toppings are available in 4 variants – bacon, black olives, pepperoni and sausage; and finally cheese available in 3 types – Cheddar, American, and Swiss. How many various types of pizzas can be made if a customer has the choice of not choosing either of toppings or cheese?

A. 3
B. 9
C. 12
D. 36
E. 60

A.  3
 B.  9
 C.  12
 D.  36
 E.  60

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apurv09 · Accepted Answer

we can also try one more method.

Since we have an option of choosing (not choosing ) any cheese or topping.We can take this as extra option.

eg. now no. of toppings =5 (including the no choice option)
now of types of cheese=4(including the no choice option)

so, the total ways=3x5x4= 60

pushpitkc · Answer

EgmatQuantExpert  - Is there a mistake in the question stem?

EgmatQuantExpert · Answer

Hi,
Can you specify what mistake you are indicating?

pushpitkc · Answer

The highlighted portion - I'm not so sure, but the meaning is not clear.

EgmatQuantExpert · Answer

This indicates while making a choice, a customer may choose one of the types of toppings and/or one of the types of cheese. However he may also choose not to include any toppings or cheese as his choice. Hope this clears.

EgmatQuantExpert · Answer

Solution

Given:  
 • Number of varieties for
 o Pizza crust = 3
o Toppings = 4
o Cheese = 3 
• One have the choice of not choosing either of toppings or cheese

To find:  
 • Number of ways pizza can be customized

Approach and Working:   
There are 4 possible cases:
 • Choice of only crust, which can be done in  ^3C_1  = 3 ways
• Choice of crust and toppings, which can be done in  ^3C_1 * ^4C_1  = 3 * 4 = 12 ways
• Choice of crust and cheese, which can be done in  ^3C_1 * ^3C_1  = 3 * 3 = 9 ways
• Choice of crust, toppings, and cheese, which can be done in  ^3C_1 * ^4C_1 * ^3C_1  = 3 * 4 * 3 =36 ways 
Therefore, the total number of ways pizza can be customized = 3 + 12 + 9 + 36 = 60 ways

Hence, the correct answer is option E.

Answer: E

4d · Answer

Hi,

has the choice of not choosing either of toppings or cheese?

has the choice of not choosing toppings  OR  not choosing cheese .
Hence he needs to choose one of those .

Choice of crust and toppings = 3*4 = 12 ways
Choice of crust and cheese = 3*3 = 9 ways
Choice of crust, toppings, and cheese = 3*4*3 = 36 ways

Answer must be 57 ways

PreiteeRanjan · Answer

Number of varieties for
 Pizza crust = 3
 Toppings = 4
 Cheese = 3
 One have the choice of not choosing either of toppings or cheese
SO 1 VERITY OF CRUST WITH 1 VERITY OF TOPPINGS WILL HAVE 4 CHOICES(3 CHEESE AND 1 ADDED BKZ SOMEONE CAN EVEN CHOOSE NO CHEESE).
SIMILARLY 1 VERITY OF CRUST WITH 4 VERITY OF TOPPINGS WILL HAVE 20 CHOICES(5*4).5 BKZ SOMEONE CAN EVEN CHOOSE NO TOPPINGS ATALL.
BUT SINCE CRUST IS MANDATORY,TOTAL COMBINATIONS POSSIBLE=3*5*4=60
 OA-E

800Dreamer · Answer

Hi,
I dont understand the 36 ways concept. why we are taking all the variants here?

ScottTargetTestPrep · Answer

The customer has 3 choices of crust, 5 choices of toppings (either one of the 4 toppings or none) and 4 choices of cheese (either one of the 3 types or none). Thus, a total of 3 x 5 x 4 = 60 different pizzas can be ordered.

Answer: E

Kinshook · Answer

Given: 
1. A pizza can be assembled from given choices, with customers' preferences. 
2. The crust is available in 3 varieties – cheese burst, classic, and wheat thin; 
3. toppings are available in 4 variants – bacon, black olives, pepperoni and sausage; 
4. and finally cheese available in 3 types – Cheddar, American, and Swiss.

Asked: How many various types of pizzas can be made if a customer has the choice of not choosing either of toppings or cheese?

Choices for crust = 3
Choices for toppings = 4 + 1 = 5
Choices for cheese = 3 + 1 = 4

Number of types of pizzas can be made if a customer has the choice of not choosing either of toppings or cheese = 3*5*4 = 60

IMO E

mandy0rhtdm · Answer

The language of this question is very confusing.
Where is it written that their can not be two toppings on a pizza or two types of cheese ? or three toppings ?

darunp · Answer

Another way:

work out the initial combinations:
3 ways to choose crust, 4 ways to choose toppings and 3 ways to choose cheese
total combinations =  3*4*3  = 36 ways

since more options are provided, there must be >36 ways, and the only answer is E

bumpbot · Answer

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A pizza can be assembled from given choices, with customer’s preferenc

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