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Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4805**

WE:**Business Development (Energy and Utilities)**

Depending on the night, a pizza restaurant offers anywhere
[#permalink]
Updated on: 12 Jan 2018, 15:22

2

Expert Reply

3

Bookmarks

Question Stats:

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

_________________

Indicate all possible values.

A. 35

B. 42

C. 56

D. 84

E. 210

F. 252

G. 504

Drill 1

Question: 13

Page: 361

Question: 13

Page: 361

Show: :: OA

A, B, D

_________________

Sandy

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Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4805**

WE:**Business Development (Energy and Utilities)**

Re: Depending on the night, a pizza restaurant offers anywhere
[#permalink]
Updated on: 12 Jan 2018, 15:21

1

Expert Reply

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.

_________________

Sandy

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

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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Try our free Online GRE Test

Re: Depending on the night, a pizza restaurant offers anywhere
[#permalink]
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.

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

Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4805**

WE:**Business Development (Energy and Utilities)**

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

Expert Reply

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.

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

_________________

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Re: Depending on the night, a pizza restaurant offers anywhere
[#permalink]
07 Oct 2021, 01:55

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

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.

Why divide by (1 x 2 x 3) ?

Re: Depending on the night, a pizza restaurant offers anywhere
[#permalink]
07 Oct 2021, 08:55

Expert Reply

koala 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 C. And when the pizza place has nine toppings, Sam has (9 × 8 × 7) ÷ (1 × 2 × 3) = 84 options, choice D.

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.

Why divide by (1 x 2 x 3) ?

see our combination chapter https://greprepclub.com/forum/gre-quant ... 18819.html

gmatclubot

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