To determine how many different combinations of 2 players can be selected from a basketball team consisting of 9 players, we can use the formula for combinations. The formula to calculate combinations is:
C(n, r) = n! / (r!(n – r)!)
In this case, n is the total number of players (9), and r is the number of players to be selected (2). Using this formula, we can substitute:
- n = 9
- r = 2
Now, applying the values to the combination formula:
C(9, 2) = 9! / (2!(9 – 2)!)
This simplifies to:
C(9, 2) = 9! / (2! * 7!)
Here, we can simplify further because the 9! can be expressed as 9 x 8 x 7!. The 7! in the numerator and denominator will cancel out, resulting in:
C(9, 2) = (9 x 8) / (2!)
Next, we calculate 2!, which is:
2! = 2 x 1 = 2
Substituting this back into our equation gives:
C(9, 2) = (9 x 8) / 2
Calculating this yields:
C(9, 2) = 72 / 2 = 36
Therefore, the coach can select 2 players from a basketball team of 9 players in 36 different ways.