How many ways to choose 3 cards

[emma007]

Hi i need help with these two problems , i have submitted it two times to my teacher and both time it was wrong ,it is confusing me up

Can you please help me in this regard

Assume cards are not replaced

Separate the 12 face cards from the rest of the deck. Assume that the remaining cards have been shuffled. Select THREE cards from the pile of face cards

1. How many ways are there of selecting one of each face card from the pile?
   
2. How many ways are there of selecting three of the same face cards (i.e., 3 jacks, 3 queens, or 3 kings) from the pile

?

Thanks in advance

 

[berkeman]

You need to show some of your work in order for us to help you. We do not supply answers to homework and coursework here on the PF.

Can you show us what you have tried so far? Then we can give you some hints on where you are going wrong...

 

[emma007]

I wrote 4*4*4=64 for the first part and for the second part i used 4+4+4=12 both of the answers are wrong


4*4*4=64 , as among 4 kings we can select 1 king in 4 ways similarly for others i did this and teacher said its wrong

We can select 3 cards of kings by 4C3 and similarly for others but this is also wrong

 

[bel]

Well, you have to consider how many ways there are to choose the required 12 cards from the deck as well.

 

[berkeman]

Assume cards are not replaced

What effect does this constraint have on the selection odds?

It sounds like you have these cards:

J, Q, K -- Spades
J, Q, K -- Clubs
J, Q, K -- Hearts
J, Q, K -- Diamonds

Right? So for the first question, you draw the first card. Then what are the odds of selecting a different face card on the 2nd draw (careful with the pool of cards left to draw out of)? And then assuming that you got a different face card on the 2nd draw, what are the odds of getting yet a different face card on the last draw? See how this works?

 

[berkeman]

Well, you have to consider how many ways there are to choose the required 12 cards from the deck as well.

That's not the way that I read his version of the question, but I could be wrong. It sounded like you just started with the 12 face cards...

 

[bel]

Oh, I see, my mistake, I read it wrong, sorry.

 

[berkeman]

1. How many ways are there of selecting one of each face card from the pile?
   
2. How many ways are there of selecting three of the same face cards (i.e., 3 jacks, 3 queens, or 3 kings) from the pile

?

Oh rats. I just realized that I misread the questions. Sorry about that.

They are asking "how many ways", not "what is the probability".

Okay, starting with the same list that I showed, you just have to add up the number of ways of combining the cards as asked. So you list the combinations:

J1, Q1, K1
J1, Q2, K1
etc...