Final answer:
To find the number of possible bridge hands containing 4 spades, 6 diamonds, 1 club, and 2 hearts, calculate the combinations of each suit and multiply them together: C(13,4) for spades, C(13,6) for diamonds, C(13,1) for clubs, and C(13,2) for hearts.
Step-by-step explanation:
The question is asking for the number of possible bridge hands with a specific combination of suits: 4 spades, 6 diamonds, 1 club, and 2 hearts. To calculate this, we need to use combinations because the order of the cards in the hand does not matter.
Firstly, select 4 spades from the 13 available, which can be done in C(13,4) ways. Then select 6 diamonds from the 13 available, which can be done in C(13,6) ways. Select 1 club from the 13 available clubs, which is simply C(13,1). Lastly, select 2 hearts from the 13 available hearts, which is C(13,2) ways.
Finally, multiply these combinations together to obtain the total number of possible hands:
- C(13,4) for spades
- C(13,6) for diamonds
- C(13,1) for clubs
- C(13,2) for hearts
The calculation is:
C(13,4) × C(13,6) × C(13,1) × C(13,2)