9 balls in a hat. balls are numbered 1-9. you choose 3 balls. how many possible combinations are there?
s5
To find the number of possible combinations when choosing 3 balls out of 9, we can use the concept of combinations. The formula for combinations is:
C(n, r) = n! / (r!(n - r)!)
Where:
- n is the total number of items (in this case, 9 available balls).
- r is the number of items chosen (in this case, 3 balls).
Let's calculate it step by step:
First, calculate the factorial of 9:
9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362,880
Next, calculate the factorial of 3:
3! = 3 × 2 × 1 = 6
Now, calculate the factorial of (9 - 3), which is 6:
6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
Using the formula, we can substitute the values:
C(9, 3) = 9! / (3!(9 - 3)!)
= 362,880 / (6 * 720)
= 362,880 / 4,320
= 84
Therefore, there are 84 possible combinations when choosing 3 balls out of 9.