Question

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 1

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.

$^{40}C_5=\dfrac{40!}{5!\times 35!}=658008$

(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

$^{37}C_2=\dfrac{37!}{2!\times 35!}=666$

Hence, a) 658008, b) 666.