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A pizza can be assembled from given choices, with customer’s preferenc
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29 May 2018, 01:48
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E
Difficulty:
65% (hard)
Question Stats:
54% (02:02) correct 46% (01:59) wrong based on 165 sessions
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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?
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29 May 2018, 05:59
EgmatQuantExpert wrote:
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
EgmatQuantExpert - Is there a mistake in the question stem?
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Re: A pizza can be assembled from given choices, with customer’s preferenc
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29 May 2018, 06:08
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EgmatQuantExpert wrote:
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
The highlighted portion - I'm not so sure, but the meaning is not clear.
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Re: A pizza can be assembled from given choices, with customer’s preferenc
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29 May 2018, 06:26
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EgmatQuantExpert wrote:
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?
pushpitkc wrote:
The highlighted portion - I'm not so sure, but the meaning is not clear.
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. _________________
Re: A pizza can be assembled from given choices, with customer’s preferenc
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31 May 2018, 01:52
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
Re: A pizza can be assembled from given choices, with customer’s preferenc
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12 May 2019, 03:39
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
Re: A pizza can be assembled from given choices, with customer’s preferenc
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25 May 2019, 06:40
EgmatQuantExpert wrote:
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
Hi, I dont understand the 36 ways concept. why we are taking all the variants here?
Re: A pizza can be assembled from given choices, with customer’s preferenc
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25 Aug 2019, 18:44
EgmatQuantExpert wrote:
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
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.
Re: A pizza can be assembled from given choices, with customer’s preferenc
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26 Aug 2019, 10:16
EgmatQuantExpert wrote:
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
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
Re: A pizza can be assembled from given choices, with customer’s preferenc
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26 Aug 2019, 11:30
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 ?
EgmatQuantExpert wrote:
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?
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54% (02:02) correct 
