Question

A basketball team has 12 players and the coach wants to pick which 5 players will start today's game. How many combinations are there for the coach to choose from?

A. 867
B. 1,248
C. 25
D. 792

Answer 1

95,040÷120 =792......... it's d

Answer 2

D. 792.

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)=(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)=(12!)/(5!(12-5)!)`

`C(12,5)=(12!)/(5!*7!)`

`C(12,5)=(12*11*10*9*8*7!)/(5*4*3*2*1*7!)`

`C(12,5)=(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.