Last visit was: 19 May 2024, 09:03 It is currently 19 May 2024, 09:03
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A fortune-teller uses 22 Major Arcana Tarot cards to perform

User avatar
devilmirror
Manager
Manager
Joined: 04 Jan 2006
Posts: 102
Own Kudos [?]: 98 [0]
Given Kudos: 0
Send PM
A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   Updated on: 07 Oct 2008, 09:06
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Hide Show timer Statistics
A fortune-teller uses 22 Major Arcana Tarot cards to perform fortune telling. She will pick 3 cards to look at querent's past, present, and futuer. A card will have different meaning if it is reversed. How many possible ways can the fortune-teller read the fortune?

A) 1,540
B) 9,240
C) 12,320
D) 73,920
E) 79,464

Bonus: Same question. If she picks 10 cards, how many ways can she read the fortune?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!

Originally posted by devilmirror on 06 Oct 2008, 22:34.
Last edited by devilmirror on 07 Oct 2008, 09:06, edited 2 times in total.
User avatar
scthakur
Director
Director
Joined: 17 Jun 2008
Posts: 614
Own Kudos [?]: 444 [0]
Given Kudos: 0
Send PM
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   06 Oct 2008, 23:34
For the original question, the answer will be 44P3 = 79464.

If she picks 10 cards, the answer will be 44P10.
User avatar
devilmirror
Manager
Manager
Joined: 04 Jan 2006
Posts: 102
Own Kudos [?]: 98 [0]
Given Kudos: 0
Send PM
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   07 Oct 2008, 09:07
Do you guys all agree with the above solution? 8-)
User avatar
vr4indian
Manager
Manager
Joined: 22 Sep 2008
Posts: 63
Own Kudos [?]: 89 [0]
Given Kudos: 0
Send PM
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   08 Oct 2008, 23:05
Please confirm the answer

I think E is right one.. here order will matter so we need to use P instead of C and reverse means we need to just double the card..
User avatar
devilmirror
Manager
Manager
Joined: 04 Jan 2006
Posts: 102
Own Kudos [?]: 98 [1]
Given Kudos: 0
Send PM
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   10 Oct 2008, 00:24
1
Kudos
devilmirror wrote:
A fortune-teller uses 22 Major Arcana Tarot cards to perform fortune telling. She will pick 3 cards to look at querent's past, present, and futuer. A card will have different meaning if it is reversed. How many possible ways can the fortune-teller read the fortune?

A) 1,540
B) 9,240
C) 12,320
D) 73,920
E) 79,464

Bonus: Same question. If she picks 10 cards, how many ways can she read the fortune?


The answer is D.

First card; 22 cards available and 2 possible interpretations = 22 x 2
Second card; 21 cards available and 2 possible interpretations = 21 x 2
Third card; 20 cards available and 2 possible interpretations = 20 x 2

Therefore, n(events) = (22x2)(21x2)(20x2) = 73,920

OR
n(events) = (\(2^3\))(P(22,3) = (8)(22x21x20) = 73,920

The answer is D.
User avatar
scthakur
Director
Director
Joined: 17 Jun 2008
Posts: 614
Own Kudos [?]: 444 [0]
Given Kudos: 0
Send PM
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   10 Oct 2008, 00:32
devilmirror wrote:
devilmirror wrote:
A fortune-teller uses 22 Major Arcana Tarot cards to perform fortune telling. She will pick 3 cards to look at querent's past, present, and futuer. A card will have different meaning if it is reversed. How many possible ways can the fortune-teller read the fortune?

A) 1,540
B) 9,240
C) 12,320
D) 73,920
E) 79,464

Bonus: Same question. If she picks 10 cards, how many ways can she read the fortune?


The answer is D.

First card; 22 cards available and 2 possible interpretations = 22 x 2
Second card; 21 cards available and 2 possible interpretations = 21 x 2
Third card; 20 cards available and 2 possible interpretations = 20 x 2

Therefore, n(events) = (22x2)(21x2)(20x2) = 73,920

OR
n(events) = (\(2^3\))(P(22,3) = (8)(22x21x20) = 73,920

The answer is D.


I am puzzled. If three cards are used to tell past, present and future, will the order of these cards not matter?
User avatar
devilmirror
Manager
Manager
Joined: 04 Jan 2006
Posts: 102
Own Kudos [?]: 98 [0]
Given Kudos: 0
Send PM
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   10 Oct 2008, 00:37
devilmirror wrote:

Bonus: Same question. If she picks 10 cards, how many ways can she read the fortune?


n(events) = (2^10)(P(22,10))
= (1024)( 22! / (22-10)! ) = (1024)(22! / 12!) = (1024)(22x21x20x...x13)

= 2,402,866,180,915,200
= 2.4 thousand trillions
= 2.4 quadrillion ways

:shock: :shock: :shock:

I guess fortune tellers will never run out of their stories.
User avatar
devilmirror
Manager
Manager
Joined: 04 Jan 2006
Posts: 102
Own Kudos [?]: 98 [0]
Given Kudos: 0
Send PM
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   10 Oct 2008, 00:45
scthakur wrote:
I am puzzled. If three cards are used to tell past, present and future, will the order of these cards not matter?


Because the order of card is matter. That's why we use permutation.

Permutation: P(22,3) = 22 x 21 x 20 = 9,240

Note:
Combination: C(22,3) = 22 x 21 x 20 / 3! = 22 x 7 x 10 = 1,540
User avatar
scthakur
Director
Director
Joined: 17 Jun 2008
Posts: 614
Own Kudos [?]: 444 [0]
Given Kudos: 0
Send PM
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   10 Oct 2008, 01:43
devilmirror wrote:
scthakur wrote:
I am puzzled. If three cards are used to tell past, present and future, will the order of these cards not matter?


Because the order of card is matter. That's why we use permutation.

Permutation: P(22,3) = 22 x 21 x 20 = 9,240

Note:
Combination: C(22,3) = 22 x 21 x 20 / 3! = 22 x 7 x 10 = 1,540



Then, where am I going wrong in my interpretation?
There are 22 cards and each card has two faces. Hence, there are a total of 44 cards to choose from. If I have to choose 3 out of 44 cards then the possible ways could be 44P3.
User avatar
AmitGUPTA
Intern
Intern
Joined: 10 Aug 2008
Posts: 33
Own Kudos [?]: 13 [0]
Given Kudos: 0
Send PM
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   10 Oct 2008, 02:09
scthakur wrote:
devilmirror wrote:
scthakur wrote:
I am puzzled. If three cards are used to tell past, present and future, will the order of these cards not matter?


Because the order of card is matter. That's why we use permutation.

Permutation: P(22,3) = 22 x 21 x 20 = 9,240

Note:
Combination: C(22,3) = 22 x 21 x 20 / 3! = 22 x 7 x 10 = 1,540



Then, where am I going wrong in my interpretation?
There are 22 cards and each card has two faces. Hence, there are a total of 44 cards to choose from. If I have to choose 3 out of 44 cards then the possible ways could be 44P3.


If you Assume number of cards is 22x2 = 44 , due to 2 faces than permutations of chossing a card out of a pack of 44 is different. Now you have only 22 cards to choose and each have 2 faces. Hope it clear your doubt !
User avatar
scthakur
Director
Director
Joined: 17 Jun 2008
Posts: 614
Own Kudos [?]: 444 [0]
Given Kudos: 0
Send PM
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   10 Oct 2008, 02:45
AmitGUPTA wrote:
If you Assume number of cards is 22x2 = 44 , due to 2 faces than permutations of chossing a card out of a pack of 44 is different. Now you have only 22 cards to choose and each have 2 faces. Hope it clear your doubt !



Thanks Amit. I know what mistake I made.
User avatar
sudhanshu_arora
Intern
Intern
Joined: 01 Nov 2005
Posts: 25
Own Kudos [?]: 2 [0]
Given Kudos: 0
Location: New jersey
Send PM
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink] A fortune-teller uses 22 Major Arcana Tarot cards to perform   10 Oct 2008, 03:10
Good work devilmirror ....

Just reminded me of concepts of permutation that is order is important in permutation.. and in this case order is important.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: A fortune-teller uses 22 Major Arcana Tarot cards to perform [#permalink]
10 Oct 2008, 03:10
Moderators:
Bunuel
Math Expert
93337 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts