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#### Raerin

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- Oct 7, 2013

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- Oct 7, 2013

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- Oct 7, 2013

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13C5 * 13C6 * 13C2 = 172,262,376What if the question asked instead:

How many bridge hands include 5 cards of hearts, 6 cards of spades and 2 cards of diamonds?

Wold you be able answer that?

If my question is the same as this one then my textbook's answer key is wrong. The textbook says the answer is 4 xxx, xxx, xxx

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Yes, good! That is correct, but this is for one specific combination of suits only.13C5 * 13C6 * 13C2?

If my question is the same as this one then my textbook's answer key is wrong.

Now you want to make it general. You want to multiply this by the number of ways to choose 3 suits from 4.

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I realized after I left that we need to find the permutations, not the combinations regarding the four suits, since order matters in this case because there are a different number of each suit. Hence, the number $N$ of the described bridge hands is:Yes, good! That is correct, but this is for one specific combination of suits only.

Now you want to make it general. You want to multiply this by the number of ways to choose 3 suits from 4.

\(\displaystyle N=\frac{4!}{(4-3)!}\cdot{13 \choose 5}\cdot{13 \choose 6}\cdot{13 \choose 2}=4134297024\)