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

[diceyfume]

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

 

[arildno]

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?

 

[diceyfume]

2, i guess?

 

[arildno]

2, i guess?

Do not guess, think.

 

[diceyfume]

ok 2 ... coz there are 4 kings in a deck of 52 cards...

 

[arildno]

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?

 

[tiny-tim]

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 ​

 

[diceyfume]

2 if the king of spades is included and 1 if it is not.

 

[arildno]

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.

 

[diceyfume]

since there's only 4 of them …

call them a b c and d, and write out all the possible pairs ​

6 , ab, bc, cd, ad, ac, bd

 

[arildno]

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?

 

[diceyfume]

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..

 

[diceyfume]

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?

 

[tiny-tim]

6 possibles for king right? and for queen how many?

d'oh! …

call them A B C and D, and list the ways!​

 

[diceyfume]

for the queen, abc,bcd, cda? am i corrct?

 

[tiny-tim]

for the queen, abc,bcd, cda? am i corrct?

Nooo

 

[diceyfume]

abc,bcd, cda, abd... it's 4?

 

[arildno]

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?

 

[diceyfume]

abc. abd, cda, bcd, it's 4?

 

[tiny-tim]

abc,bcd, cda, abd... it's 4?

Yes, it's 4 …

but you can't list them like that in an exam , so what formula would you show the examiner (and what formula for the 6 ways of the kings)?

 

[arildno]

abc. abd, cda, bcd, it's 4?

That's right.
Read my previous post on how to finish the exercise.

 

[diceyfume]

10, am i correct? am i going to add them?

 

[tiny-tim]

10, am i correct? am i going to add them?

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

can you list them? ​

 

[arildno]

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?

 

[diceyfume]

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

 

[arildno]

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.

 

[diceyfume]

abc. abd, cda, bcd, ab, ac, ad, bc, bd, cd

 

[tiny-tim]

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?

 

[arildno]

abc. abd, cda, bcd, ab, ac, ad, bc, bd, cd

?

 

[tiny-tim]

abc. abd, cda, bcd, ab, ac, ad, bc, bd, cd

erm … try using different letters for kings and queens!