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.

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=(40!)/(5!* 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=(37!)/(2!* 35!)=666`

Hence, a) 658008, b) 666.