Playing cards word problem: 5 cards are drawn from a normal deck of cards....

MathLearner2016

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5 cards are drawn from a normal deck of cards.
a) What are the odds that drawn was 1 five card and 2 three cards?
b) What are the odds that 3 of the cards were of the same suit?
 
5 cards are drawn from a normal deck of cards.
a) What are the odds that drawn was 1 five card and 2 three cards?
b) What are the odds that 3 of the cards were of the same suit?
What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you! ;)
 
5 cards are drawn from a normal deck of cards.
a) What are the odds that drawn was 1 five card and 2 three cards?
b) What are the odds that 3 of the cards were of the same suit?

There are \(\displaystyle \dbinom{4}{1}\cdot\dbinom{4}{2}\cdot\dbinom{44}{2}\) ways to have a five card hand in which there is one ace and two threes.

There are \(\displaystyle \dbinom{52}{5}\) possible five card hands.
 
There are \(\displaystyle \dbinom{4}{1}\cdot\dbinom{4}{2}\cdot\dbinom{44}{2}\) ways to have a five card hand in which there is one ace and two threes.

There are \(\displaystyle \dbinom{52}{5}\) possible five card hands.

Could you verify my result:
(C4,1 x C4,2 x C44,2) / (C52,5) = (4 x 6 x 946) / (2598960) = (22704) / (2598960) = 0.0087
 
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You are just fishing for answers. I done.
I'm sorry you feel that way, my reasoning is very flawed but let me explain:

How many ways can you chose a suit?

There are 4 suits and you can choose one in four (C4,1).

How many ways can you chose exactly three of that suit?

There are 13 cards in a suit and 3 must be chosen (C13,3).

I know, I'm terrible at this. :(
 
5 cards are drawn from a normal deck of cards.
a) What are the odds that drawn was 1 five card and 2 three cards?
b) What are the odds that 3 of the cards were of the same suit?
Part b) Forget probability and counting for one moment. If I asked you to pick 5 cards from a deck with 3 cards of a single suit how would you do it? List every decision which you have to make!
 
Part b) Forget probability and counting for one moment. If I asked you to pick 5 cards from a deck with 3 cards of a single suit how would you do it? List every decision which you have to make!
... thinking
 
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You need to think what decisions you need to make on how to pick 5 cards from a deck with 3 being the same suit?

What would the 1st thing be that you would have to decide on??
We have 4 colors, 13 in each of which 3 must be drawn. Then there's 5 out of 52 being drawn...
 
We have 4 colors, 13 in each of which 3 must be drawn. Then there's 5 out of 52 being drawn...
1st you need to pick a suit (in how many ways can you do that?), AND then you pick the 3 cards of that suit (in how many ways can you do that?) AND then ....

Edit: meant to say 1st you pick the denomination.
 
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I think I meant:

4C1 * 13C3 / 52C5
I think maybe you're wrong because of what I said--sorry about that. So I'll say it again.

1st you pick a denomination AND then you pick 3 cards from that denomination AND then................................????????
 
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