Respuesta :
Answer: a) 658008, b) 666.
Step-by-step explanation:
Since we have given that
Total number of computers = 40
Number of failed computers = 5
(a) How many possibilities are there for the five that fail?
We will use "Combination" to find all 5 failed.
[tex]^{40}C_5=\dfrac{40!}{5!\times 35!}=658008[/tex]
(b) Suppose that 3 of the computers in the network have a copy of a particular file. How many sets of failures wipe out all the copies of the file?
So, number of computers failed left = 5-3 =2
Total number of computers = 40-3=37
So, the number of set of failures wipe out would be
[tex]^{37}C_2=\dfrac{37!}{2!\times 35!}=666[/tex]
Hence, a) 658008, b) 666.
The number of possibilities that exists for the five that fail is; 658008
How to solve probability combination?
We are given;
Total number of computers = 40
Number of failed computers = 5
(A) To find the number of possibilities that are there for the five that fail, we will use combination method. Thus;
40C5 = 40!/(5! * (40 - 5)!)
>> 40!/(5! * 35!)
>> 658008
B) If we assume that 3 of the computers in the network have a copy of a particular file. Then;
number of computers failed that are left = 5 - 3 = 2
Thus;
Total number of computers = 40-3=37
Finally, the number of set of failures wipe out would be; 37C2 = 40!/(5! * (40 - 5)!)
>> 40!/(5! * 35!)
>> 658008
Read more about Probability Combination at;https://brainly.com/question/4658834
