Thread Closed

Combinatorics Problem

 
Share Thread
Apr10-05, 02:05 PM   #1
 

Combinatorics Problem


Suppose you play a game of cards in which only four cards are dealt from a standard deck of 52 cards. How many ways are there to obtain three of a kind? (3 cards of the same rank and 1 card of a different rank, for example 3 tens and 1 queen.)

Could someone help me with how to do this problem? I tried doing 4C3 x 13 x 52C1, which was obviously wrong. :/ Any help would be appreciated.
PhysOrg.com science news on PhysOrg.com

>> Leading 3-D printer firms to merge in $403M deal (Update)
>> LA to give every student an iPad; $30M order
>> CIA faulted for choosing Amazon over IBM on cloud contract
Apr10-05, 02:24 PM   #2
 
You can choose first card in 52 different ways. You can choose the next two (same of a kind as the first one) in 3 * 2 ways. And the last card, in 49 different ways.
Apr10-05, 10:34 PM   #3
 
Recognitions:
Science Advisor Science Advisor
Quote by blue_soda025
Suppose you play a game of cards in which only four cards are dealt from a standard deck of 52 cards. How many ways are there to obtain three of a kind? (3 cards of the same rank and 1 card of a different rank, for example 3 tens and 1 queen.)

Could someone help me with how to do this problem? I tried doing 4C3 x 13 x 52C1, which was obviously wrong. :/ Any help would be appreciated.
The standard 52 cards contain 13 different ranks of 4 cards each.
For any given rank, there are C(4,3) combinations of 3 cards chosen from the rank's 4 cards. Since there are 13 different ranks, a total of {13*C(4,3)} possible combinations of {3 cards from the same rank} exist. Finally, there remain {(52 - 4) = 48} cards in the 12 other (different) ranks from which to choose the final card. Hence:
{Total Combinations of "3-of-a-Kind" from std 52 Cards} = {13*C(4,3)}*(48) = (2496)


~~
Thread Closed

Similar discussions for: Combinatorics Problem
Thread Forum Replies
combinatorics problem Precalculus Mathematics Homework 3
Combinatorics....evil problem!! Calculus & Beyond Homework 1
Combinatorics problem Calculus & Beyond Homework 1
combinatorics-next problem with numbers Introductory Physics Homework 6
Combinatorics problem Introductory Physics Homework 2