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 3 solutions by consc198, JWG, ikleyn:
Answer by consc198(59)   (Show Source):
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.
Answer by ikleyn(53937)  (Show Source):
You can put this solution on YOUR website! .
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?
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The answer in the post by @consc198 is FATALLY and TOTALLY wrong.
For a correct solution, see what follows.
The coach can select one center from two centers in 2 different ways.
The coach can select two forwards from five forwards in C(5,2) =  = 10 different ways.
The coach can select two guards from four guards in C(4,2) =  = 6 different ways.
So, according to the fundamental counting principle , the coach can combine the starting team in
2*10*6 = 120 different ways.
ANSWER. The coach can select the starting team in 120 different ways.
Solved correctly.
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I just said it several times before that @consc198 has no qualification to be a tutor.
In many cases, he does not understand what he writes and simply deceives readers without any hesitation.
Such people must be disgracefully expelled from the profession.
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