PLEASE HELP:
How many ways are there to choose 3 cards from a standard deck of 52, if all three cards must be different suits? (Assume that the order of the cards don't matter)

Question

PLEASE HELP: 
How many ways are there to choose 3 cards from a standard deck of 52, if all three cards must be different suits? (Assume that the order of the cards don't matter)

anonymous · Answer

How many suits are there in a deck of cards?

anonymous · Answer

4 Suits

anonymous · Answer

13 cards per suit

anonymous · Answer

How many ways are there to choose 3 of the 4 suits?

anonymous · Answer

(That's the first step)

anonymous · Answer

4 c 3 = 4

anonymous · Answer

good

anonymous · Answer

Now, the second step is to determine how many ways there are to choose a card of one suit. First, how many cards of there of a suit?

anonymous · Answer

13

anonymous · Answer

How many ways are there to choose one of those 13 cards?

anonymous · Answer

One of thirteen? Well, 1, 13 c 1, if you want.

anonymous · Answer

13c1 = 13 ways to choose 1 of 13 cards.

anonymous · Answer

Whoops, xD

anonymous · Answer

My mistake, I meant 13.

anonymous · Answer

Now repeat the process twice more. How many ways are there to pick a card of a second suit? A third suit?

anonymous · Answer

Wouldn't it also be 13 for the second suit and 13 for the third suit?

anonymous · Answer

Yes!

anonymous · Answer

Now, use the fundamental counting principle to tell me. How many ways are there to pick 3 different suits and then pick one card from each of those three suits?

anonymous · Answer

What does the fundamental counting principle tell us about how to count the total number ways to do something?

anonymous · Answer

To multiply your choices? (per say)

anonymous · Answer

Yes!

anonymous · Answer

So I think it would be (4 c 3) x (3 c 1) = 12, or 4 x 3 = 12

anonymous · Answer

Partly correct. Partly incorrect. 4 c 3 is good. 3 c 1 is not good.

anonymous · Answer

The 4 c 3 part is choosing the three suits. 3 c 1 is not necessary for that.

anonymous · Answer

Really just multiply all the numbers we got together (4,13,13,13)

anonymous · Answer

So 8788?

anonymous · Answer

Yes.

anonymous · Answer

Because you have 4 cases (of picking 3 suits out of 4) and then you have a choice of 13 cards to "represent" each suit?

anonymous · Answer

13^3*

anonymous · Answer

13 for each suit

anonymous · Answer

yes. 13 cards to represent each suit, three times. yes 13^3

anonymous · Answer

Okay, alright, thanks a ton.

anonymous · Answer

np