Answer:
D. 792.
Step-by-step explanation:
We have been given that a basketball team has 12 players and the coach wants to pick which 5 players will start today's game.
We will use combinations formula to solve our given problem. \(C(n,r)=\frac{n!}{r!(n-r)!}\), where,
n = Number of total items,
r = Number of items being chosen at a time.
Upon substituting our given values in combinations formula we will get,
\(C(12,5)=\frac{12!}{5!(12-5)!}\)
\(C(12,5)=\frac{12!}{5!*7!}\)
\(C(12,5)=\frac{12*11*10*9*8*7!}{5*4*3*2*1*7!}\)
\(C(12,5)=\frac{12*11*10*9*8}{5*4*3*2}\)
\(C(12,5)=11*9*8\)
\(C(12,5)=792\)
Therefore, the coach can choose from 792 combinations and option D is the correct choice.
