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devilmirror
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A fortune-teller uses 22 Major Arcana Tarot cards to perform Updated on: 07 Oct 2008, 09:06
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.
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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?



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A fortune-teller uses 22 Major Arcana Tarot cards to perform 06 Oct 2008, 23:34
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For the original question, the answer will be 44P3 = 79464.

If she picks 10 cards, the answer will be 44P10.
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A fortune-teller uses 22 Major Arcana Tarot cards to perform 07 Oct 2008, 09:07
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Do you guys all agree with the above solution? 8-)
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vr4indian
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A fortune-teller uses 22 Major Arcana Tarot cards to perform 08 Oct 2008, 23:05
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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..
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A fortune-teller uses 22 Major Arcana Tarot cards to perform 10 Oct 2008, 00:24
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devilmirror
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?
Show more

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.
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A fortune-teller uses 22 Major Arcana Tarot cards to perform 10 Oct 2008, 00:32
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devilmirror
devilmirror
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.
Show more

I am puzzled. If three cards are used to tell past, present and future, will the order of these cards not matter?
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A fortune-teller uses 22 Major Arcana Tarot cards to perform 10 Oct 2008, 00:37
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devilmirror


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

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.
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A fortune-teller uses 22 Major Arcana Tarot cards to perform 10 Oct 2008, 00:45
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scthakur

I am puzzled. If three cards are used to tell past, present and future, will the order of these cards not matter?
Show more

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
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A fortune-teller uses 22 Major Arcana Tarot cards to perform 10 Oct 2008, 01:43
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devilmirror
scthakur

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
Show more


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.
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A fortune-teller uses 22 Major Arcana Tarot cards to perform 10 Oct 2008, 02:09
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scthakur
devilmirror
scthakur

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.
Show more

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 !
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A fortune-teller uses 22 Major Arcana Tarot cards to perform 10 Oct 2008, 02:45
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AmitGUPTA
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 !
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Thanks Amit. I know what mistake I made.
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A fortune-teller uses 22 Major Arcana Tarot cards to perform 10 Oct 2008, 03:10
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Good work devilmirror ....

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



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