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# An honor card is a face card or an ace. How many bridge hands contain exactly k honor cards for k = 1,...13.?

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- PuzzlingLv 79 months agoFavorite Answer
There are 3 face cards and 1 ace in each suit for a total of 16 "honor" cards. There would then be 36 "non-honor" cards.

A bridge hand consists of 13 cards. The number of ways to form a hand with 'k' honor cards would be calculated as follows:

- From the 16 honor cards, pick k

- From the 36 non-honor cards, pick 13-k

C(16,k) * C(36,13-k)

You can calculate that value for k=0 to 13, though they seem to only want 1 to 13 for some reason.

Here's a table for each value of k

0 = 2,310,789,600

1 = 20,026,843,200

2 = 72,096,635,520

3 = 142,344,639,360

4 = 171,340,769,600

5 = 132,177,165,120

6 = 66,848,221,440

7 = 22,282,740,480

8 = 4,851,887,040

9 = 673,873,200

10 = 57,177,120

11 = 2,751,840

12 = 65,520

13 = 560

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