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At a particular pizza shop, a pizza can be created from any combinatio

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At a particular pizza shop, a pizza can be created from any combinatio  [#permalink]

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New post 08 Apr 2016, 02:46
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Question Stats:

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At a particular pizza shop, a pizza can be created from any combination of 3 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?

A. 6
B. 35
C. 120
D. 450
E. 740

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Re: At a particular pizza shop, a pizza can be created from any combinatio  [#permalink]

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New post 08 Apr 2016, 21:41
1
2
Number of possible ways to select 1 type of spice = 3c1 = 3
Number of possible ways to select 2 types of cheese = 4c2 = 6
(Here we can pick our answer as D- 450 since it is the only answer that is divisible by 3*6= 18 , but most likely on the GMAT there will be more another answer that will be divisible by 18 )
Number of possible ways to select 4 types of meat but without pepperoni and anchovies together
= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together
= 7c4 - 5c2
=35 - 10
=25

Possible ways to garnish the pizza are available to the customer = 3*6 * 25
=450

Answer D
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Re: At a particular pizza shop, a pizza can be created from any combinatio  [#permalink]

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New post 19 Sep 2018, 06:32
Skywalker18 wrote:
Number of possible ways to select 1 type of spice = 3c1 = 3
Number of possible ways to select 2 types of cheese = 4c2 = 6
(Here we can pick our answer as D- 450 since it is the only answer that is divisible by 3*6= 18 , but most likely on the GMAT there will be more another answer that will be divisible by 18 )
Number of possible ways to select 4 types of meat but without pepperoni and anchovies together
= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together
= 7c4 - 5c2
=35 - 10
=25

Possible ways to garnish the pizza are available to the customer = 3*6 * 25
=450

Answer D


How did you calculate total number of ways in which pepperoni and anchovies together as 10.I did not understand 5c2.Please help.
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Re: At a particular pizza shop, a pizza can be created from any combinatio  [#permalink]

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New post 19 Sep 2018, 09:07
AnkitOrYadav wrote:
Skywalker18 wrote:
Number of possible ways to select 1 type of spice = 3c1 = 3
Number of possible ways to select 2 types of cheese = 4c2 = 6
(Here we can pick our answer as D- 450 since it is the only answer that is divisible by 3*6= 18 , but most likely on the GMAT there will be more another answer that will be divisible by 18 )
Number of possible ways to select 4 types of meat but without pepperoni and anchovies together
= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together
= 7c4 - 5c2
=35 - 10
=25

Possible ways to garnish the pizza are available to the customer = 3*6 * 25
=450

Answer D


How did you calculate total number of ways in which pepperoni and anchovies together as 10.I did not understand 5c2.Please help.

You need to select 4 meat out of 7. So if you consider pepperoni and anchovies together , 2 out 4 slot is filled. Remaining 2 slot can filled with remaining 5 options.
Therefore , 5c2
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Re: At a particular pizza shop, a pizza can be created from any combinatio   [#permalink] 19 Sep 2018, 09:07
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