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Depending on the night, a pizza restaurant offers anywhere

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CEO
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GRE 1: 323 Q167 V156
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Depending on the night, a pizza restaurant offers anywhere [#permalink] New post 30 Dec 2017, 14:00
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Depending on the night, a pizza restaurant offers anywhere from seven to nine different choices of toppings. Sam wants a pizza with three toppings. Which of the following could be the number of different ways that Sam can order his pizza with three different toppings?

Indicate all possible values.

A. 35
B. 42
C. 56
D. 84
E. 210
F. 252
G. 504

Drill 1
Question: 13
Page: 361


[Reveal] Spoiler: OA
A, B, D
[Reveal] Spoiler: OA

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Last edited by sandy on 12 Jan 2018, 15:22, edited 2 times in total.
CEO
CEO
User avatar
Joined: 07 Jun 2014
Posts: 3018
GRE 1: 323 Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 53

Kudos [?]: 873 [0], given: 154

CAT Tests
Re: Depending on the night, a pizza restaurant offers anywhere [#permalink] New post 08 Jan 2018, 16:16
Expert's post
Explanation

This problem is about combinations, because order doesn’t matter. On a night when the pizza place offers only seven toppings, Sam has (7 × 6 × 5) ÷ (1 × 2 × 3) = 35 options, choice A.

When the pizza place has eight toppings, Sam has (8 × 7 × 6) ÷ (1 × 2 × 3) = 56 options, choice C. And when the pizza place has nine toppings, Sam has (9 × 8 × 7) ÷ (1 × 2 × 3) = 84 options, choice D.
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Last edited by sandy on 12 Jan 2018, 15:21, edited 2 times in total.
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Re: Depending on the night, a pizza restaurant offers anywhere [#permalink] New post 08 Jan 2018, 19:29
sandy wrote:
Explanation

This problem is about combinations, because order doesn’t matter. On a night when the pizza place offers only seven toppings, Sam has (7 × 6 × 5) ÷ (1 × 2 × 3) = 35 options, choice A.

When the pizza place has eight toppings, Sam has (8 × 7 × 6) ÷ (1 × 2 × 3) = 56 options, choice B. And when the pizza place has nine toppings, Sam has (9 × 8 × 7) ÷ (1 × 2 × 3) = 84 options, choice D.


Correction in calculation it should be 56 instead of 42 and hence the option will be C
CEO
CEO
User avatar
Joined: 07 Jun 2014
Posts: 3018
GRE 1: 323 Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 53

Kudos [?]: 873 [0], given: 154

CAT Tests
Re: Depending on the night, a pizza restaurant offers anywhere [#permalink] New post 12 Jan 2018, 15:20
Expert's post
svijay wrote:
sandy wrote:
Explanation

This problem is about combinations, because order doesn’t matter. On a night when the pizza place offers only seven toppings, Sam has (7 × 6 × 5) ÷ (1 × 2 × 3) = 35 options, choice A.

When the pizza place has eight toppings, Sam has (8 × 7 × 6) ÷ (1 × 2 × 3) = 56 options, choice B. And when the pizza place has nine toppings, Sam has (9 × 8 × 7) ÷ (1 × 2 × 3) = 84 options, choice D.


Correction in calculation it should be 56 instead of 42 and hence the option will be C

Fixed it! Thanks
_________________

Sandy
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Re: Depending on the night, a pizza restaurant offers anywhere   [#permalink] 12 Jan 2018, 15:20
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