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 :wink:

[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 :wink:
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! :rolleyes: …

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 :rolleyes:

[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 :wink:, 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? :wink:

[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 dont know the formula, u guys just help me how to solve it...can u just give the formula to me then? pls

[arildno]

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

[arildno]

Use, for example, upper case for kings, lower case for queens..

[diceyfume]

actually i was not around when our lecturer took this up so its kinda hard for me to answer these homeworks... im doing research works but i end up to this forum.

[diceyfume]

abc. abd, cda, bcd, AB, AC, AD, BC, BD,CD

[arildno]

You have 6 sets of two kings, 4 sets of queens.

If it is hard for you to know whether you should add, subtract, divide, exponentiate, multiply or possibly take the root of 6 with 4 in order to know how many different combinations you can make (a combination consisting of 1 kingset AND a queenset), then your problem is not with your homework, but that you still struggle with the maths most 8-year olds master.

[tiny-tim]

actually i was not around when our lecturer took this up so its kinda hard for me to answer these homeworks... im doing research works but i end up to this forum.

it would have helped if you'd said that in the first place …

ok, look at http://en.wikipedia.org/wiki/Combination

[diceyfume]

:shy: thanks anyway.. im insulted... thanks.. this forum is nice though...

[diceyfume]

im good in math its just that i didnt know the formulas...thanks

[arildno]

im good in math
No, you are not.
its just that i didnt know the formulas
You don't need to. Use your brain, instead of waiting to be spoonfed answers.

Furthermore, it is not an "insult" to you to say you struggle with the maths of 8-year olds, it happens to be an unfortunate fact.

Stating facts does not constitute an insult, however unpleasant those facts might be.

[diceyfume]

how will i cancel or delete my account?

[tiny-tim]

how will i cancel or delete my account?

diceyfume, just look at that wikipedia article, and then try the question again …

if you don't understand something in the article, then ask us …

but please don't expect us to do the question for you :smile:

[diceyfume]

thanks tiny-tim... tomorrow will be better, i need to get some sleep...

[cristo]

A time out is certainly needed here, since this is doing noone any good. Diceyfume: have a think about the problem, and come back tomorrow with a clearer head. I am locking this thread for ~12 hours, to enable all to clear their heads.