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# Paula and Anna decided to order a pizza with 6 slices all w

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 806
Paula and Anna decided to order a pizza with 6 slices all w [#permalink]

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28 Mar 2017, 10:23
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Difficulty:

45% (medium)

Question Stats:

62% (01:25) correct 38% (01:18) wrong based on 75 sessions

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Q.

Paula and Anna decided to order a pizza with 6 slices all with different toppings and 2 pastries – 1 Chocolate and 1 Caramel. In how many different ways can Paula and Anna choose their food if they each eat three pizza slices and 1 pastry?

A. 24
B. 36
C. 40
D. 80
E. 120

Thanks,
Saquib
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[Reveal] Spoiler: OA

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 806
Paula and Anna decided to order a pizza with 6 slices all w [#permalink]

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28 Mar 2017, 10:24
The official solution has been posted. Looking forward to a healthy discussion..
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Last edited by EgmatQuantExpert on 31 Mar 2017, 02:29, edited 1 time in total.
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Joined: 28 Jan 2016
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Re: Paula and Anna decided to order a pizza with 6 slices all w [#permalink]

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28 Mar 2017, 11:27
each girl chooses 3 slices from 6 and 1 of 2 cakes. This means: 3C6*2
e-GMAT Representative
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Re: Paula and Anna decided to order a pizza with 6 slices all w [#permalink]

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31 Mar 2017, 00:09
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Expert's post
EgmatQuantExpert wrote:
Q.

Paula and Anna decided to order a pizza with 6 slices all with different toppings and 2 pastries – 1 Chocolate and 1 Caramel. In how many different ways can Paula and Anna choose their food if they each eat three pizza slices and 1 pastry?

A. 24
B. 36
C. 40
D. 80
E. 120

Solution

Given:
• There are $$6$$ slices of pizza.
o Paula and Anna will have $$3$$ each.
• There are $$2$$ pastries.
o Paula and Anna will have $$1$$ each.

Approach:

• The number of ways in which $$3$$ pizza each can be selected for Paula and Anna $$= ^6C_3 * ^3C_3 = \frac{720}{36} = 20$$
• The number of ways in which $$1$$ pastry each can be selected for Paula and Anna $$= ^2C_1* ^1C_1 = 2$$
• As they will have both the pizza AND the pastry, we need to multiply the above two values to get the total number of ways to choose the food $$= 20*2 = 40$$.
• Hence the correct answer is Option C.

Thanks,
Saquib
Quant Expert
e-GMAT

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 806
Re: Paula and Anna decided to order a pizza with 6 slices all w [#permalink]

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31 Mar 2017, 00:15
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Expert's post
foled wrote:
each girl chooses 3 slices from 6 and 1 of 2 cakes. This means: 3C6*2

Hey Foled,

Your answer is absolutely correct. But shouldn't you write $$^3C_6$$ as $$^6C_3 = \frac{{6!}}{{3!.3!}}$$?? [$$^nC_R = \frac{n!}{{r!.(n-r)!}}$$]

Thanks,
Saquib
Quant Expert
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Director
Joined: 12 Nov 2016
Posts: 790
Re: Paula and Anna decided to order a pizza with 6 slices all w [#permalink]

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22 Apr 2017, 18:01
EgmatQuantExpert wrote:
Q.

Paula and Anna decided to order a pizza with 6 slices all with different toppings and 2 pastries – 1 Chocolate and 1 Caramel. In how many different ways can Paula and Anna choose their food if they each eat three pizza slices and 1 pastry?

A. 24
B. 36
C. 40
D. 80
E. 120

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

One thing that I don't understand about this question is that it asks, I think, what are the possible number of arrangments that can be made for both Anna and Paula? If Paula was choosing 3 of 6 distinct slices and 1 of 2 distinct pastries then there would certainly be 40 possible arrangments. Though what are the number of arrangments considering both Paula and Anna? Wouldn't that be more?
Intern
Joined: 29 Jan 2017
Posts: 46
Re: Paula and Anna decided to order a pizza with 6 slices all w [#permalink]

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22 Apr 2017, 19:05
EgmatQuantExpert wrote:
EgmatQuantExpert wrote:
Q.

Paula and Anna decided to order a pizza with 6 slices all with different toppings and 2 pastries – 1 Chocolate and 1 Caramel. In how many different ways can Paula and Anna choose their food if they each eat three pizza slices and 1 pastry?

A. 24
B. 36
C. 40
D. 80
E. 120

Solution

Given:
• There are $$6$$ slices of pizza.
o Paula and Anna will have $$3$$ each.
• There are $$2$$ pastries.
o Paula and Anna will have $$1$$ each.

Approach:

• The number of ways in which $$3$$ pizza each can be selected for Paula and Anna $$= ^6C_3 * ^3C_3 = \frac{720}{36} = 20$$
• The number of ways in which $$1$$ pastry each can be selected for Paula and Anna $$= ^2C_1* ^1C_1 = 2$$
• As they will have both the pizza AND the pastry, we need to multiply the above two values to get the total number of ways to choose the food $$= 20*2 = 40$$.
• Hence the correct answer is Option C.

Thanks,
Saquib
Quant Expert
e-GMAT

Aiming to score Q50 or higher in GMAT Quant? Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Register

Can you please explain why you would do 6c3 * 6c3 (I understand there are two entities to consider, but the other would get whichever is remaining)? I believe it has the same result as 6c3.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 806
Re: Paula and Anna decided to order a pizza with 6 slices all w [#permalink]

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24 Apr 2017, 21:36
mrdlee23 wrote:

Can you please explain why you would do 6c3 * 6c3 (I understand there are two entities to consider, but the other would get whichever is remaining)? I believe it has the same result as 6c3.

Yes mrdlee23, you are correct that the other will get whatever is remaining and 3C3 is equal to 1.

I had written that so that it is clear to everyone that for the other person, there is only 1 way to choose the remaining. Therefore 6C3 * 3C3 = 6C3 only.

Regards,
Saquib
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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 806
Re: Paula and Anna decided to order a pizza with 6 slices all w [#permalink]

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24 Apr 2017, 21:39
Nunuboy1994 wrote:

One thing that I don't understand about this question is that it asks, I think, what are the possible number of arrangments that can be made for both Anna and Paula? If Paula was choosing 3 of 6 distinct slices and 1 of 2 distinct pastries then there would certainly be 40 possible arrangments. Though what are the number of arrangments considering both Paula and Anna? Wouldn't that be more?

Hey,

The question asks us just the number of ways of selecting the slices and pastries and we do not need to consider the arrangement. Also, understand that once say Paula chooses whatever she wants, Anna has to take whatever is left. And we don't need to consider separately the arrangement of Paula and Anna here. The 6C3 *3C3, takes into consideration, all the ways in which Paula and Anna can choose the slices.

Regards,
Saquib
Quant Expert
e-GMAT
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Re: Paula and Anna decided to order a pizza with 6 slices all w   [#permalink] 24 Apr 2017, 21:39
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# Paula and Anna decided to order a pizza with 6 slices all w

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