Question

I need a formula for solving this. Not the answer a formula. A basketball team has ten players. 5 are gaurds, 3 are centers, 2 are forwards. If there has to be two gaurds two centers and one forward how many possible combinations are there?

Answer 1

\[\sqrt{?} \] Also what does this mean?

Answer 2

second question first. it means the positive square root

Answer 3

so for example
\[\sqrt{25}=5\]

Answer 4

now for first question. you need 2 guards. the number of way to pick two people from a set of 5 is
\[\frac{5\times 4}{2}=10\]
this is sometimes written as 5C2 or
\[\dbinom{5}{2}\]

Answer 5

there are 3 ways to pick 2 centers from a set of 3. just like saying "how many ways can i exclude 1 of them" and there are obviously 3 ways. if you want to write 3C2=3 that is fine too

Answer 6

obviously 2 different ways to choose one forward from the 2 you have. so your "final answer" by the counting principle is \[10\times 3\times 2=60\]

Answer 7

Thanks :)