- #1

whitejac

- 169

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## Homework Statement

If you have a 52card deck and split it evenly to 4 people (a,b,c,d) then what is the probability that persons a and b have 7 spades and person c has 3 spades.

## Homework Equations

P(A) = |A|/|S|

## The Attempt at a Solution

I divided up the decks 4 ways. So Persons a and b should have 26 cards total. There's no requirement that one person have more spades than the other.

So I collected them together.

The chance that they draw 7spades out of the top of the deck should be

13/52 * 12/51 * 11/50... *7/46

Then the chance that they draw non spades should be:

39/45 * 38/44... * 20/26

For there are still 6 spades in the deck and 19 carded must be drawn.

I would do this again for person C, he would be allowed to draw:

6/25 * 5/24 * 4/23 *19/22 * 18/21... * 11/14.

I may have messed up that last fraction.

Does my logic make sense..?