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Math Challenge I-B Winter 2022-23 Question 2.24

 
 
LinEdward的头像
Math Challenge I-B Winter 2022-23 Question 2.24
LinEdward - 2022年12月10日 Saturday 18:04
 
For this question regarding 52 cards for blackjack, are the 10's and face cards considered the same or different, and are numbers with different colors and/or suits considered the same or different?


Thanks,

Edward

 
LensmireJohn的头像
Re: Math Challenge I-B Winter 2022-23 Question 2.24
LensmireJohn - 2022年12月12日 Monday 10:28
 

All $52$ cards in a standard deck of cards are different, so we need to take that account for counting problems with decks of cards.

In case more details are needed for a standard deck of cards. There are:

  • 13 ranks/values: $2, 3, 4, \ldots, 10$, $J$ (Jack), $Q$ (Queen), $K$ (King), and $A$ (Ace)
  • 4 suits: Hearts and Diamonds (both red), Spades and Clubs (both black)

Each of the $13\times 4 = 52$ cards has one rank and one suit. So there is one "4 of Spaces", one "King of Clubs", etc. Hence, there are $4$ of each rank (one for each suit) and $13$ of each suit (one for each rank).

Hope this helps!


LinEdward的头像
Re: Math Challenge I-B Winter 2022-23 Question 2.24
LinEdward - 2022年12月12日 Monday 18:20
 

Thank you very much!

ZhuKevin的头像
Re: Math Challenge I-B Winter 2022-23 Question 2.24
ZhuKevin - 2022年12月13日 Tuesday 18:59
 

GOOD JOB