SOLUTION: Please help me solve this. Suppose 5 cards are dealt from a standard deck of 52 cards. How many unique 5-card hands are possible?

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Question 1066282: Please help me solve this.
Suppose 5 cards are dealt from a standard deck of 52 cards. How many unique 5-card hands are possible?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How many different sets of 5 cards each can be formed from a standard deck of 52 cards?
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The 1st choice is 1 of 52.
Then 1 of 51, etc.
--> 52*51*50*49*48 = 311857200
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But, choosing cards A,B,C,D & E is the same as B,A,D,E & C.
--> 120 (5*4*3*2*1) ways to get the same 5 cards.
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311857200/120 = 2598960 sets

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Each set is a "combination" of 52 items taken 5 at a time.

It is classical combinations in the combinatoric sense.


On Combinations, see the lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
    - OVERVIEW of lessons on Permutations and Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".