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In how many ways 8 different tickets can be distributed [#permalink]
20 Nov 2009, 06:46

Expert's post

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Difficulty:

85% (hard)

Question Stats:

47% (02:33) correct
53% (01:23) wrong based on 96 sessions

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.

Re: Sharing tickets. [#permalink]
22 Nov 2009, 15:06

2

This post received KUDOS

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.

Re: Sharing tickets. [#permalink]
22 Nov 2009, 15:30

Expert's post

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.

Re: Sharing tickets. [#permalink]
23 Nov 2009, 12:23

1

This post received KUDOS

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? _________________

Re: Sharing tickets. [#permalink]
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.

Re: Sharing tickets. [#permalink]
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!!!! _________________

Re: Sharing tickets. [#permalink]
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.

Re: Sharing tickets. [#permalink]
26 Nov 2009, 10:39

Expert's post

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. _________________

Re: Sharing tickets. [#permalink]
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?

Re: Sharing tickets. [#permalink]
29 May 2012, 08:00

Expert's post

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.

Re: In how many ways 8 different tickets can be distributed [#permalink]
06 Oct 2013, 11:26

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Re: Sharing tickets. [#permalink]
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.

gmatclubot

Re: Sharing tickets.
[#permalink]
08 Oct 2013, 03:31