SOLUTION: A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of (a) four hearts and one spade? (b) three red card

Question 520629: A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of (a) four hearts and one spade? (b) three red cards and two black cards? (c) at least 3 face cards? (d) 2 aces and 2 face cards?
Found 2 solutions by stanbon, edjones:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards.
-----------------------
How many different hands are there consisting of
(a) four hearts and one spade?
# of ways to get 4 hearts: 13C4 = 715
# of ways to get 1 spade: 13C1 = 13
---
Total # of ways = 715*13 = 9295
=================================================
(b) three red cards and two black cards?
# of ways to get 3 red = 26C3 = 2600
# of ways to get 2 black = 26C2 = 325
---
Total # of ways = 845,000
==================================================
(c) at least 3 face cards?
There are 12 face cards:
3 face cards: 12C3*40C2 = 220*780
+ 4 face cards: 12C4*40C1 = 495*40
+ 5 face cards: 12C5*40C0 = 792*1
---
Total # = 171600 + 19800 + 792 = 192,192
=======================================
(d) 2 aces and 2 face cards?
# of ways to get 2 aces: 4C2 = 6
# of ways to get 2 face cards: 12C2 = 66
---
Total # of ways = 6*66 = 396
============================================
Cheers,
Stan H.
===============

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
a)13C4*13C1=715*13=9295
b)26C3*26C2=2600*325=845000
c)12C3*40C2+12C4*40C1+12C5=171600+19800+792=192192
d)4C2*12C2*36C1=156816
.
Ed
RELATED QUESTIONS
A poker hand consists of five cards dealt from a deck of 52. How many diferent poker... (answered by checkley71)
A poker hand consists of 5 cards consists of 5 cards dealt from an ordinary deck of 52... (answered by tomlaidlaw)
A standard poker hand consists of five cards dealt from a deck of 52. How many different... (answered by checkley71)
Please help me with the following problem: A poker hand consistes of 5 cards dealt from... (answered by stanbon)
A poker hand consists of five cards from a standard deck of 52. How many poker hands are... (answered by robertb)
If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, how many different (answered by Edwin McCravy)
PLEASE HELP ME... A poker hand consists of 5 cards from a deck of 52 cards. How... (answered by scianci)
How many different 5 card hands can be dealt from a standard deck of 52 playing... (answered by Edwin McCravy)
In a 5-card poker game a player is dealt 5 cards. How many poker hands are possible for... (answered by stanbon)