Final answer:
There are N factorial (N!) valid serial schedules for a net of N transactions, as each transaction can be processed in any order relative to the others, resulting in a permutation of the transactions.
Step-by-step explanation:
The number of valid serial schedules for a net of N transactions is 2N factorial. In the context of databases, a serial schedule is a sequence of operations where transactions are processed one after another without overlap. When there are N transactions, each can be processed first, second, and so on, up to Nth. Hence, the number of permutations of these transactions is N factorial (N!). For example, with three transactions (T1, T2, T3), the valid serial schedules would include T1-T2-T3, T1-T3-T2, T2-T1-T3, T2-T3-T1, T3-T1-T2, and T3-T2-T1. These are all the ways you can order three items, hence the use of factorials.
In the context of databases, a serial schedule is a sequence of operations executed by multiple transactions, where the operations of each transaction appear in the same order as in its original schedule. A serial schedule ensures that the transactions are executed in isolation without any interleaving of their operations. The number of valid serial schedules for a net of N transactions can be calculated using the formula: 2N.For example, if there are 3 transactions in the net, the number of valid serial schedules would be 23 = 8