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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
5
00:00
A
B
C
D
E
Difficulty:
75% (hard)
Question Stats:
50% (02:09) correct 50% (02:03) wrong based on 112 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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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.
_________________
You've got what it takes, but it will take everything you've got
Re: A pizza can be assembled from given choices, with customer’s preferenc
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29 May 2018, 06:26
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
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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?
gmatclubot
Re: A pizza can be assembled from given choices, with customer’s preferenc
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25 May 2019, 06:40
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50% (02:09) correct 
