# Combinations question

• Feb 16th 2009, 06:19 AM
struck
Combinations 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 AM
Quote:

Originally Posted by struck
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?

52C8 as there is no condition .
• Feb 16th 2009, 06:44 AM
struck
The answer given to me in the book is 5.346x10^13 but 52C8 is 752,538,150. (Doh)
• Feb 16th 2009, 07:56 AM
Plato
Quote:

Originally Posted by struck
The answer given to me in the book is 5.346x10^13 but 52C8 is 752,538,150. (Doh)

Well look at this: $\displaystyle 52^8 =53459728531456= 5.346\times 10^{13}$.
• Feb 16th 2009, 07:58 AM
Soroban
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 AM
struck
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 AM
struck
Still looking for ideas :(