SOLUTION: The traveling squad for a basketball team consists of two centers, five forwards, and four guards. In how many ways can the coach select a starting team of one center, two forwards

Click here to see ALL problems on Probability-and-statistics

Question 46732: The traveling squad for a basketball team consists of two centers, five forwards, and four guards. In how many ways can the coach select a starting team of one center, two forwards, and two guards?
Found 2 solutions by consc198, JWG:
Answer by consc198(59) (Show Source):
You can put this solution on YOUR website!
The answer is 20

Answer by JWG(21) (Show Source):
You can put this solution on YOUR website!
Hopefully someone that knows better can confirm or correct, but I think the answer is 120. Here is how I got there:

Center: 2 ways to select one center
Forward: 5C2 or 10 ways to select two forwards
Guard: 4C2 or 6 ways to select two guards

For the forwards and guards, I used what is called a Combinations Formula. One can look up how to use it on Wikipedia or use the =COMBIN(x,y) function in Excel. The long hand version that one would have to use to solve by hand is 5!/2!*(5-2)! As you can see, for forwards I had '5' for the number of available forwards I had to choose from and '2' for the amount that I would select from the available group. Now onto the rest of the solution...

I multiply the possibilities that I have for each position: 2*10*6 which equals 120.