Respuesta :
Answer:
2,052,086,400.
Step-by-step explanation:
Permutation
Pr = n! / (n-r)!
30P5 = 30! / (30-5)
30P5 = 30x29x28x27x26x25! / 25!
(Just cancel the 25! on the numerator and denominator for easier solving.)
30P5 = 30x29x28x27x26
30P5 = 17,100,720.It is not the final answer because we can still arrange the 5 winners.
5! = 5×4×3×2×1 = 12017,100,720 × 120 = 2,052,086,400
We will see that the total number of different combinations in which the prizes can be awarded is C = 17,100,720
How to find the total number of combinations?
First, we need to find all the selections. In this case we have:
- prize 1
- prize 2
- prize 3
- prize 4
- prize 5.
Now we need to count the number of options for each of these selections, the number of options will depend on the number of students in the class.
- prize 1: 30 options here
- prize 2: 29 options (because one student already won the 1st prize)
- prize 3: 28 options
- prize 4: 27 options
- prize 5: 26 options.
The total number of different combinations is equal to the product between the numbers of options, we will have:
C = 30*29*28*27*26 = 17,100,720
If you want to learn more about combinations, you can read:
https://brainly.com/question/11732255