How many 3 members committee can be selected from a class of 20 students?
20C3
To find the number of 3-member committees that can be selected from a class of 20 students, we can use the concept of combinations.
The number of ways to select a committee of 3 members from a group of 20 students can be calculated using the formula for combinations:
C(n, r) = n! / (r!(n-r)!)
where n represents the total number of elements and r represents the number of elements to be selected.
In this case, we want to find the number of ways to select 3 students from a group of 20, so n = 20 and r = 3.
Plugging these values into the formula, we get:
C(20, 3) = 20! / (3!(20-3)!)
Simplifying:
C(20, 3) = 20! / (3! * 17!)
Now, let's break down the calculation:
20! = 20 * 19 * 18 * 17!
3! = 3 * 2 * 1 = 6
17! = 17 * 16 * 15 * ... * 3 * 2 * 1
Substituting these values back into the formula:
C(20, 3) = (20 * 19 * 18 * 17!) / (6 * 17!)
Notice that (17!) cancels out. This simplifies the formula to:
C(20, 3) = (20 * 19 * 18) / (6)
Evaluating the expression:
C(20, 3) = (20 * 19 * 18) / 6
C(20, 3) = 1,140
Therefore, there are 1,140 possible 3-member committees that can be selected from a class of 20 students.