Thread: Need help with a few questions.

So we choose the 3 suits our hand consists of: 4C3.

Now we choose 5 of the 13 cards of the first suit: 13C5

Now we choose 6 of the 13 cards of the second suit: How do we do this?

Now we choose 2 of the 13 cards of the last suit: How do we do this?

Originally Posted by Jame

So we choose the 3 suits our hand consists of: 4C3.

Now we choose 5 of the 13 cards of the first suit: 13C5

Now we choose 6 of the 13 cards of the second suit: How do we do this?

Now we choose 2 of the 13 cards of the last suit: How do we do this?

So 1287, 1716, 78.

Then multiply them all to get a hand?

Yes, we multiply

4C3 * 13C5 * 13C6 * 13C2

Originally Posted by Jame

Yes, we multiply

4C3 * 13C5 * 13C6 * 13C2

Ok I got 689 049 504, which is the final answer?

Yep, that is the answer. You can also leave it 4C3 * 13C5 * 13C6 * 13C2 if you want.

Originally Posted by Jame

Yep, that is the answer. You can also leave it 4C3 * 13C5 * 13C6 * 13C2 if you want.

Okay, thanks so much for the help, both you and emakarov!

I'm sorry I was actually mistaken in my answer for 2). Since we have different amounts of each suit (5,6,2), we must choose each suit individually. So instead of 4C3, its 4*3*2 (or 4!)

The rest of the answer is the same.

Example: a hand with "5 hearts, 6 spades and 2 diamonds" is different then a hand with "5 diamonds, 6 hearts and 2 spades"
(order of the suits does in fact matter here)

If we had a different breakdown of suits (like 5,5,3). We would have to choose the two suits with the 5 cards (4C2), then choose the suit with 3 cards (2C1)

The only time we would choose the suits all together is if each card had the same breakdown (e.g. (3,3,3))

Originally Posted by Jame

I'm sorry I was actually mistaken in my answer for 2). Since we have different amounts of each suit (5,6,2), we must choose each suit individually. So instead of 4C3, its 4*3*2 (or 4!)

The rest of the answer is the same.

Example: a hand with "5 hearts, 6 spades and 2 diamonds" is different then a hand with "5 diamonds, 6 hearts and 2 spades"
(order of the suits does in fact matter here)

If we had a different breakdown of suits (like 5,5,3). We would have to choose the two suits with the 5 cards (4C2), then choose the suit with 3 cards (2C1)

The only time we would choose the suits all together is if each card had the same breakdown (e.g. (3,3,3))

Changed, thanks for letting me know!