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Permutation and Combination

guest17

New member
Joined
Mar 24, 2012
Messages
3
Bridge is a card game that deals players 13 card hands. How many bridge hands contain exactly 5 spades?

I got (4C1)x (13C5) but it's not the correct answer.. help!
 

wjm11

Senior Member
Joined
Nov 13, 2004
Messages
1,417
Bridge is a card game that deals players 13 card hands. How many bridge hands contain exactly 5 spades?

I got (4C1)x (13C5) but it's not the correct answer.. help!
Thanks, PKA. I was thinking 5-card poker hands, not a bridge hand obviously!
 
Last edited:

pka

Elite Member
Joined
Jan 29, 2005
Messages
7,688
Bridge is a card game that deals players 13 card hands. How many bridge hands contain exactly 5 spades?.. help!
There are thirteen spades and thirty-nine non-spades. 13-5=8
Now what is your answer?
 

soroban

Elite Member
Joined
Jan 28, 2005
Messages
5,588
Hello, guest17!

Bridge is a card game that deals players 13-card hands.
How many bridge hands contain exactly 5 Spades?

I got ([SUB]4[/SUB]C[SUB]1[/SUB]) x ([SUB]13[/SUB]C[SUB]5[/SUB]) but it's not the correct answer. . Of course not!

You changed the game to Poker (5-card hands).
And you've answered the question:
. . "How many Flushes are there?"


The deck contains 13 Spades and 39 Others.
We want 5 Spades and 8 Others.

There are: .([SUB]13[/SUB]C[SUB]5[/SUB])([SUB]39[/SUB]C[SUB]8[/SUB]) hands with exactly 5 Spades.
 
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