There are 5 students in a small class. To make a team, the names of 3 of them will be drawn from a hat. How many different teams of
3 students are possible?
5C3 = ?
To find the number of different teams of 3 students possible from a class of 5, we can use a combination formula.
The combination formula is given by:
C(n, r) = n! / (r! * (n - r)!)
Where:
- n! denotes the factorial of n, which is the product of all positive integers up to n.
- r is the number of items being chosen.
- (n - r)! denotes the factorial of (n - r).
In this case, n = 5 (the number of students in the class) and r = 3 (the number of students being chosen for a team).
Using the combination formula:
C(5, 3) = 5! / (3! * (5 - 3)!)
Calculating the factorials:
5! = 5 x 4 x 3 x 2 x 1 = 120
3! = 3 x 2 x 1 = 6
(5 - 3)! = 2! = 2 x 1 = 2
Plugging in the values:
C(5, 3) = 120 / (6 * 2) = 120 / 12 = 10
Therefore, there are 10 different teams of 3 students possible from a class of 5.