A teacher is choosing 4 students from a class of 30 to represent the class at a science fair. In how many ways can the teacher choose the students?
400
To find the number of ways the teacher can choose 4 students from a class of 30, we can use the concept of combinations.
The number of ways to choose k elements from a set of n elements is given by the formula for combinations: nCk = n! / (k! * (n - k)!)
In this case, the teacher wants to choose 4 students from a class of 30. So, plug in the values into the formula:
n = 30 (total number of students)
k = 4 (number of students to be chosen)
30C4 = 30! / (4! * (30 - 4)!)
Now we can calculate this using the factorial function.
Step 1: Calculate the factorial for each number:
30! = 30 * 29 * 28 * ... * 2 * 1
4! = 4 * 3 * 2 * 1
26! = 26 * 25 * 24 * ... * 2 * 1
Step 2: Substitute these values into the formula:
30C4 = (30 * 29 * 28 * ... * 2 * 1) / ((4 * 3 * 2 * 1) * (26 * 25 * 24 * ... * 2 * 1))
Step 3: Simplify the expression by canceling out the common terms:
30C4 = (30 * 29 * 28 * 27) / (4 * 3 * 2 * 1)
Step 4: Evaluate the expression:
30C4 = 27,405
Therefore, there are 27,405 ways for the teacher to choose 4 students from a class of 30 to represent the class at the science fair.