How many ways can 5 student receive a grade A or E
To determine how many ways 5 students can receive a grade of either A or E, we can use the concept of combinations. Since each student can receive either an A or an E, there are 2 options for each student.
To find the total number of ways, we need to calculate the number of combinations. The formula for combinations is:
C(n, k) = n! / (k!(n - k)!)
Where:
- n is the total number of items to choose from (in this case, the number of students, which is 5).
- k is the number of items to be chosen (in this case, the number of students receiving a grade of A, which can range from 0 to 5).
Let's consider all possible values for k and calculate the total number of combinations:
For k = 0:
C(5, 0) = 5! / (0!(5 - 0)!) = 1
For k = 1:
C(5, 1) = 5! / (1!(5 - 1)!) = 5
For k = 2:
C(5, 2) = 5! / (2!(5 - 2)!) = 10
For k = 3:
C(5, 3) = 5! / (3!(5 - 3)!) = 10
For k = 4:
C(5, 4) = 5! / (4!(5 - 4)!) = 5
For k = 5:
C(5, 5) = 5! / (5!(5 - 5)!) = 1
Therefore, the total number of ways 5 students can receive a grade of either A or E is:
1 (for k = 0) + 5 (for k = 1) + 10 (for k = 2) + 10 (for k = 3) + 5 (for k = 4) + 1 (for k = 5) = 32.
Hence, there are 32 ways in which 5 students can receive a grade of either A or E.