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In how many ways 8 different tickets can be distributed

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In how many ways 8 different tickets can be distributed [#permalink] New post 20 Nov 2009, 06:46
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In how many ways 8 different tickets can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.

A. From 2 to 6 inclusive.
B. From 98 to 102 inclusive.
C. From 122 to 126 inclusive.
D. From 128 to 132 inclusive.
E. From 196 to 200 inclusive.
[Reveal] Spoiler: OA

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Re: Sharing tickets. [#permalink] New post 20 Nov 2009, 07:57
Sorry but I do not understand the answer choices. From x to y ?? is it the number of ways?
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Re: Sharing tickets. [#permalink] New post 20 Nov 2009, 08:04
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Re: Sharing tickets. [#permalink] New post 20 Nov 2009, 09:26
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Possibilities

J 8 6 4 2 0

B 0 2 4 6 8

# of ways 8C8 8C6 8C4 8C2 8C0

1+28+70+28+1 = 128 Answer is D.
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Re: Sharing tickets. [#permalink] New post 22 Nov 2009, 06:25
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Tickets can be distributed in the following ways:

{8,0} - 8C8=1
{6,2} - 8C6*2C2=28
{4,4} - 8C4*4C4=70
{2,6} - 8C2*6C6=28
{0,8} - 8C8=1

Total # of ways=1+28+70+28+1=128

Answer is D. (Note that this is my question so no OA).

+1 to atish, for the right solution.
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Re: Sharing tickets. [#permalink] New post 22 Nov 2009, 11:52
Nice.... loved this one!

I solved it but it took too much time!
Surely I would have jumped
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Re: Sharing tickets. [#permalink] New post 22 Nov 2009, 15:06
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Bunuel wrote:
In how many ways 8 different tickets can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.

(A) From 2 to 6 inclusive.
(B) From 98 to 102 inclusive.
(C) From 122 to 126 inclusive.
(D) From 128 to 132 inclusive.
(E) From 196 to 200 inclusive.


Again what is wrong with my logic?

I can select 0 tickets for Jane and all 8 tickets for Bill. I could repeat the selection and reverse the order between Bill and Jane.

I can select 2 tickets for Jane and 6 tickets for Bill. I could repeat the selection and reverse the order between Bill and Jane.

I can select 4 tickets for Jane and 4 tickets for Bill. I could repeat the selection and reverse the order between Bill and Jane.

Overall 2[ 8C0 + 8C2 + 8C4 ] = 198.
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Re: Sharing tickets. [#permalink] New post 22 Nov 2009, 15:30
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SensibleGuy wrote:
Bunuel wrote:
In how many ways 8 different tickets can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.

(A) From 2 to 6 inclusive.
(B) From 98 to 102 inclusive.
(C) From 122 to 126 inclusive.
(D) From 128 to 132 inclusive.
(E) From 196 to 200 inclusive.


Again what is wrong with my logic?

I can select 0 tickets for Jane and all 8 tickets for Bill. I could repeat the selection and reverse the order between Bill and Jane.

I can select 2 tickets for Jane and 6 tickets for Bill. I could repeat the selection and reverse the order between Bill and Jane.

I can select 4 tickets for Jane and 4 tickets for Bill. I could repeat the selection and reverse the order between Bill and Jane.

Overall 2[ 8C0 + 8C2 + 8C4 ] = 198.


Everything is right, but the red part.

8C4*4C4 is the formula counting # of ways this can be done (B-4 and J-4), we don't need to multiply this by 2.

You don't need to reverse the order in this case as ALL possible scenarios are already covered with 8C4.

You are reversing in scenario 8-0 as you can have 0-8, but in 4-4 it's only one case.

Hope it's clear.
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Re: Sharing tickets. [#permalink] New post 23 Nov 2009, 12:23
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Bunuel wrote:
Everything is right, but the red part.

8C4*4C4 is the formula counting # of ways this can be done (B-4 and J-4), we don't need to multiply this by 2.

You don't need to reverse the order in this case as ALL possible scenarios are already covered with 8C4.

You are reversing in scenario 8-0 as you can have 0-8, but in 4-4 it's only one case.

Hope it's clear.


Let me be more clear.

I can select 4 tickets of 8 in 8C4 ways. Remaining 4 tickets will be 4C4 obviously.
After selecting those 4 tickets, I have to select either Bill or Jane as the receiver of the 4 tickets in 2C1 ways. The remaining person is 1C1.
After making the two selections, all possible combinations are 8C4*4C4*2C1*1C1 = 70*2 = 140.

Is there a flaw in my selections?
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Re: Sharing tickets. [#permalink] New post 23 Nov 2009, 15:45
BarneyStinson wrote:
Bunuel wrote:
Everything is right, but the red part.

8C4*4C4 is the formula counting # of ways this can be done (B-4 and J-4), we don't need to multiply this by 2.

You don't need to reverse the order in this case as ALL possible scenarios are already covered with 8C4.

You are reversing in scenario 8-0 as you can have 0-8, but in 4-4 it's only one case.

Hope it's clear.


Let me be more clear.

I can select 4 tickets of 8 in 8C4 ways. Remaining 4 tickets will be 4C4 obviously.
After selecting those 4 tickets, I have to select either Bill or Jane as the receiver of the 4 tickets in 2C1 ways. The remaining person is 1C1.
After making the two selections, all possible combinations are 8C4*4C4*2C1*1C1 = 70*2 = 140.

Is there a flaw in my selections?


By using 8C4 exclusively, you are already counting the possibility of a specific set of 4 tickets going to either person.

For example, say you had 4 tickets, labeled A, B, C and D.

4C2 = 6
AB, CD
AC, BD
AD, BC

As you can see, it accounts for a specific set of 2 tickets, as well as the complete opposite. By multiplying by a factor of 2, you end up double-counting.
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Re: Sharing tickets. [#permalink] New post 23 Nov 2009, 15:56
AKProdigy87 wrote:
By using 8C4 exclusively, you are already counting the possibility of a specific set of 4 tickets going to either person.
For example, say you had 4 tickets, labeled A, B, C and D.

4C2 = 6
AB, CD
AC, BD
AD, BC

As you can see, it accounts for a specific set of 2 tickets, as well as the complete opposite. By multiplying by a factor of 2, you end up double-counting.


aaaarrrrggghhhhhhhh!!!! I get your point!!!! Damn my awesomeness!!!!
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Re: Sharing tickets. [#permalink] New post 24 Nov 2009, 20:10
hello, so in the end, the answer is 128 right? i got the same answer, using the same solution as atish. i'm just making sure it's the right one.

i'm also wondering as to the answer choices: why the range? shouldn't there be one and only one answer? is there a way to approximate the answer? anyone have any ideas as to approximating this? i solved the problem, but it took me about 4 minutes, which is time i wouldn't have in the actual exam.

cheers!
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Re: Sharing tickets. [#permalink] New post 26 Nov 2009, 10:39
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pochcc wrote:
hello, so in the end, the answer is 128 right? i got the same answer, using the same solution as atish. i'm just making sure it's the right one.

i'm also wondering as to the answer choices: why the range? shouldn't there be one and only one answer? is there a way to approximate the answer? anyone have any ideas as to approximating this? i solved the problem, but it took me about 4 minutes, which is time i wouldn't have in the actual exam.

cheers!


Yes, the answer is 128.

Answers are represented as ranges, because there are number of incorrect answers possible and several ranges are needed to cover them all.
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Re: Sharing tickets. [#permalink] New post 29 May 2012, 07:26
Hey bunuel the question steam says tickets are to distributed such that both get even no. correct me, isnt 0 neither even nor odd? then how can we take the case of 8,0?
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Re: Sharing tickets. [#permalink] New post 29 May 2012, 08:00
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vibhav wrote:
Hey bunuel the question steam says tickets are to distributed such that both get even no. correct me, isnt 0 neither even nor odd? then how can we take the case of 8,0?


Zero is nether positive nor negative, but zero is definitely an even number.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Or in another way: an even number is an integer of the form n=2k, where k is an integer. So for k=0 --> n=2*0=0.

Hope it's clear.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In how many ways 8 different tickets can be distributed [#permalink] New post 06 Oct 2013, 11:26
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Re: Sharing tickets. [#permalink] New post 08 Oct 2013, 03:31
Bunuel wrote:
vibhav wrote:
Hey bunuel the question steam says tickets are to distributed such that both get even no. correct me, isnt 0 neither even nor odd? then how can we take the case of 8,0?


Zero is nether positive nor negative, but zero is definitely an even number.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer except zero itself).

Or in another way: an even number is an integer of the form n=2k, where k is an integer. So for k=0 --> n=2*0=0.

Hope it's clear.



I dunno my approach is right or wrong but i get the same ans.

by applying the formula 2^(n-1) when n equals to no. of chocolates...therefore 2^(8-1)=2^7=128.
Please correct me if iam wrong.
Re: Sharing tickets.   [#permalink] 08 Oct 2013, 03:31
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