Final answer:
There are 3,747,166 possibilities for the 7 servers that fail in the network of 35 servers.
Step-by-step explanation:
The number of possibilities for the 7 servers that fail can be calculated using combinations.
Since there are 35 servers in total and 7 of them fail, we need to calculate the number of ways we can choose 7 servers from a set of 35. This can be done using the combination formula:
C(35, 7) = 35! / (7!(35-7)!)
= 35! / (7!28!) = (35 * 34 * 33 * 32 * 31 * 30 * 29) / (7 * 6 * 5 * 4 * 3 * 2 * 1)
= 3,747,166 possibilities