Suppose a network has 40 computers of which 5 fail. (a) How many possibilities are there for the five that fail? (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? That is, how many 5-subsets contain the three computers that have the file?

Answer: a) 658008, b) 666.Step-by-step explanation:Since we have given that Total number of computers = 40Number 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 =2Total number of computers = 40-3=37So, 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.