How many ways can you draw 3 queens and 2 kings from a deck of 52 cards?

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Discussion Overview

The discussion revolves around the combinatorial problem of determining the number of ways to draw 3 queens and 2 kings from a standard deck of 52 cards. Participants explore the mathematical reasoning behind combinations, specifically focusing on how to calculate the number of sets of queens and kings.

Discussion Character

  • Mathematical reasoning
  • Debate/contested
  • Homework-related

Main Points Raised

  • Participants discuss how to calculate the number of combinations of 2 kings from 4 available kings.
  • Some participants suggest that there are 2 combinations of kings, while others challenge this reasoning and prompt further logical thinking.
  • There is a proposal to list all possible pairs of kings to clarify the combinations.
  • Participants also explore how many sets of 3 queens can be formed from 4 queens, with varying responses regarding the correct number of combinations.
  • Some participants express frustration with others' approaches, suggesting a lack of effort in understanding the problem.
  • There is a mention of using different letters to represent kings and queens for clarity in combinations.
  • One participant indicates they are struggling with the material due to missing prior instruction on the topic.
  • Discussions about whether to add, subtract, or use other operations to find the total combinations arise, with some participants feeling insulted by the comments made about their understanding of math.

Areas of Agreement / Disagreement

There is no consensus on the correct number of combinations for drawing the cards, and multiple competing views remain regarding the calculations and approaches to the problem. The discussion reflects a mix of frustration and attempts to clarify mathematical reasoning.

Contextual Notes

Some participants express uncertainty about the formulas needed for solving the problem, and there are references to a lack of prior knowledge that may affect their understanding of the topic.

Who May Find This Useful

This discussion may be useful for individuals interested in combinatorial mathematics, particularly in the context of card games or probability problems, as well as those seeking to understand how to approach mathematical reasoning in problem-solving scenarios.

diceyfume
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How many ways can you draw 3 queens and 2 kings from a deck of 52 cards?
 
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You are to pick out 5 cards out of 8 possible ones; three queens out of the four possibles, and two kings out of the 4 possibles.

Start with:

Out of 4 kings, how many 2-king combinations exist?
 
2, i guess?
 
diceyfume said:
2, i guess?
Do not guess, think.
 
ok 2 ... coz there are 4 kings in a deck of 52 cards...
 
No.

Try to think again. LOGICALLY. It isn't too hard.

First sub-question: How many 2-sets of kings exist if the king of spades is to be included?

Second sub-question: How many 2-sets of kings exist if the king of spades is NOT included?
 
diceyfume said:
ok 2 ... coz there are 4 kings in a deck of 52 cards...

since there's only 4 of them …

call them A B C and D, and write out all the possible pairs :wink:​
 
2 if the king of spades is included and 1 if it is not.
 
This won't work, diceyfume.

You are obviously refusing to utilize your intellect, and are only interested in being spoonfed "answers".

I strongly advise you to quit maths, because your attitude makes you incompetent in it.
 
  • #10
tiny-tim said:
since there's only 4 of them …

call them a b c and d, and write out all the possible pairs :wink:​
6 , ab, bc, cd, ad, ac, bd
 
  • #11
diceyfume said:
6 , ab, bc, cd, ad, ac, bd

Correct. Why didn't you start doing that on your own?

Now, how many sets of three queens can you form out of 4?
 
  • #12
arildno said:
This won't work, diceyfume.

You are obviously refusing to utilize your intellect, and are only interested in being spoonfed "answers".

I strongly advise you to quit maths, because your attitude makes you incompetent in it.
i guess its 6... i posted it... thanks, i'll just try next sem..
 
  • #13
arildno said:
Correct. Why didn't you start doing that on your own?

Now, how many sets of three queens can you form out of 4?
6 possibles for king right? and for queen how many?
 
  • #14
diceyfume said:
6 possibles for king right? and for queen how many?

d'oh! :rolleyes: …

call them A B C and D, and list the ways!​
 
  • #15
for the queen, abc,bcd, cda? am i corrct?
 
  • #16
diceyfume said:
for the queen, abc,bcd, cda? am i corrct?

Nooo :rolleyes:
 
  • #17
abc,bcd, cda, abd... it's 4?
 
  • #18
diceyfume said:
abc,bcd, cda, abd... it's 4?


Right!

So, you have 6 2-sets of kings, and 4 3-sets of queens.

So, how many different combinations consisting of one king-set and one queen set can you then make?
 
  • #19
abc. abd, cda, bcd, it's 4?
 
  • #20
diceyfume said:
abc,bcd, cda, abd... it's 4?

Yes, it's 4 …

but you can't list them like that in an exam :wink:, so what formula would you show the examiner (and what formula for the 6 ways of the kings)?
 
  • #21
diceyfume said:
abc. abd, cda, bcd, it's 4?
That's right.
Read my previous post on how to finish the exercise.
 
  • #22
10, am i correct? am i going to add them?
 
  • #23
diceyfume said:
10, am i correct? am i going to add them?

If there's only 10, you can easily list them …

can you list them? :wink:​
 
  • #24
diceyfume said:
10, am i correct? am i going to add them?

If you first take the (king of spades, king of hearts)-couple, how many 3-sets of queens can it be combined with?
 
  • #25
i don't know the formula, u guys just help me how to solve it...can u just give the formula to me then? pls
 
  • #26
diceyfume said:
i don't know the formula, u guys just help me how to solve it...
That's what we are doing right now.
can u just give the formula to me then? pls

Nope.
 
  • #27
abc. abd, cda, bcd, ab, ac, ad, bc, bd, cd
 
  • #28
diceyfume said:
i don't know the formula, u guys just help me how to solve it...can u just give the formula to me then? pls

diceyfume, you're being ridiculous …

you must know some formulas for these combination problems …

what book are you working from…

what do your notes say?
 
  • #29
diceyfume said:
abc. abd, cda, bcd, ab, ac, ad, bc, bd, cd
?
 
  • #30
diceyfume said:
abc. abd, cda, bcd, ab, ac, ad, bc, bd, cd

erm :redface: … try using different letters for kings and queens!
 

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