Eight cards are selected with replacement from a standard pack of 52 playing cards, with 12 picture cards, 20 odd cards, and 20 even cards.

How many different sequences of eight cards are possible?

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- Feb 16th 2009, 06:19 AMstruckCombinations question
Eight cards are selected with replacement from a standard pack of 52 playing cards, with 12 picture cards, 20 odd cards, and 20 even cards.

How many different sequences of eight cards are possible? - Feb 16th 2009, 06:34 AMmathaddict
- Feb 16th 2009, 06:44 AMstruck
The answer given to me in the book is 5.346x10^13 but 52C8 is 752,538,150. (Doh)

- Feb 16th 2009, 07:56 AMPlato
- Feb 16th 2009, 07:58 AMSoroban
Hello, struck!

Quote:

Eight cards are selected**with replacement**from a standard decl of cards.

How many different sequences of eight cards are possible?

For each of the eight cards, there are 52 possible choices.

Answer: .$\displaystyle 52^8 \:=\:5,345972853 \times 10^{13}$

- Feb 17th 2009, 03:21 AMstruck
Ok so that makes it a permutation problem of type 'with replacement' instead of a combination problem?

A related question has got me stuck again.

(b) How many of the sequences in part (a) will contain three picture cards, three odd-numbered cards and two even-numbered cards.

Note: (a) was the original question, i.e., "How many different sequences of eight cards are possible?"

I do really have a trouble with permutations and combinations, so a little explanation in this answer will be greatly appreciated.

So points that I have noticed: (please correct if mistaken)

* There are 3 types of objects

* There are 8 objects to be selected out of the 3 types - Feb 23rd 2009, 02:13 AMstruck
Still looking for ideas :(