Mr. Jefferson has 20 students in his class. He wants to send 4 of these students to pick up books for the class.
How many combinations of 4 students can he choose?
A)5
B)80
C)4845
D)116,280
20C4
where nCr=n!/((n-r)!r!)
The answer is B
Bakhrom Khalmatov is not savage
To find the number of combinations of 4 students that Mr. Jefferson can choose, we can use the concept of combinations.
The formula to calculate combinations is given by:
C(n, r) = n! / (r! * (n-r)!)
Where:
- C(n, r) represents the number of combinations of r items chosen from a set of n items.
- n! represents the factorial of n, which is the product of all positive integers less than or equal to n.
In this case, Mr. Jefferson has 20 students in his class and wants to choose 4 students.
Using the formula for combinations:
C(20, 4) = 20! / (4! * (20-4)!)
Simplifying further:
C(20, 4) = 20! / (4! * 16!)
Calculating the factorials:
20! = 20 * 19 * 18 * .. * 2 * 1
4! = 4 * 3 * 2 * 1
16! = 16 * 15 * 14 * .. * 2 * 1
C(20, 4) = (20 * 19 * 18 * .. * 2 * 1) / (4 * 3 * 2 * 1 * 16 * 15 * 14 * .. * 2 * 1)
A lot of terms cancel out:
C(20, 4) = (20 * 19 * 18 * 17) / (4 * 3 * 2 * 1)
Simplifying further:
C(20, 4) = 4845
Therefore, the correct answer is option C) 4845.