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

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A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

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New post 29 May 2018, 00:48
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A
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Difficulty:

  75% (hard)

Question Stats:

48% (01:44) correct 52% (01:38) wrong based on 89 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?

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

To solve question 3: P&C Practice Question 3

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Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

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New post 29 May 2018, 04:59
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  [#permalink]

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New post 29 May 2018, 05:02
pushpitkc wrote:

EgmatQuantExpert - Is there a mistake in the question stem?


Hi,
Can you specify what mistake you are indicating?
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Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

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New post 29 May 2018, 05:08
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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  [#permalink]

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New post 29 May 2018, 05:26
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. :-)
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Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

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New post 31 May 2018, 00:52

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

Hence, the correct answer is option E.

Answer: E
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Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

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New post 01 Jun 2018, 06:02
1
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
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Re: A pizza can be assembled from given choices, with customer’s preferenc  [#permalink]

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New post 11 Jan 2019, 21:10
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
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Re: A pizza can be assembled from given choices, with customer’s preferenc &nbs [#permalink] 11 Jan 2019, 21:10
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