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

1. Mar 14, 2009

### diceyfume

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

2. Mar 14, 2009

### 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.

Out of 4 kings, how many 2-king combinations exist?

3. Mar 14, 2009

### diceyfume

2, i guess?

4. Mar 14, 2009

### arildno

Do not guess, think.

5. Mar 14, 2009

### diceyfume

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

6. Mar 14, 2009

### 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?

7. Mar 14, 2009

### tiny-tim

since there's only 4 of them …

call them A B C and D, and write out all the possible pairs

8. Mar 14, 2009

### diceyfume

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

9. Mar 14, 2009

### 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.

10. Mar 14, 2009

### diceyfume

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

11. Mar 14, 2009

### arildno

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. Mar 14, 2009

### diceyfume

i guess its 6... i posted it... thanks, i'll just try next sem..

13. Mar 14, 2009

### diceyfume

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

14. Mar 14, 2009

### tiny-tim

d'oh!

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

15. Mar 14, 2009

### diceyfume

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

16. Mar 14, 2009

### tiny-tim

Nooo

17. Mar 14, 2009

### diceyfume

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

18. Mar 14, 2009

### arildno

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. Mar 14, 2009

### diceyfume

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

20. Mar 14, 2009

### tiny-tim

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)?

21. Mar 14, 2009

### arildno

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

22. Mar 14, 2009

### diceyfume

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

23. Mar 14, 2009

### tiny-tim

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

can you list them?

24. Mar 14, 2009

### arildno

If you first take the (king of spades, king of hearts)-couple, how many 3-sets of queens can it be combined with?

25. Mar 14, 2009

### 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