What is the number of non-serial schedules possible containing 3 transactions…
What is the number of non-serial schedules possible containing 3 transactions of 2,3 and 4 operations respectively?
Answer: 1254 — To find the number of non-serial schedules, first calculate the total number of possible schedules for 3 transactions with 2, 3, and 4 operations…
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Correct answer: 1254
To find the number of non-serial schedules, first calculate the total number of possible schedules for 3 transactions with 2, 3, and 4 operations respectively.
The total number of schedules is given by the multinomial coefficient:
(n1 + n2 + n3)! / (n1! * n2! * n3!)
Here, n1 = 2, n2 = 3, n3 = 4, so total schedules = 9! / (2! * 3! * 4!)
Next, calculate the number of serial schedules. A serial schedule is one where all operations of one transaction are completed before another begins. For 3 transactions, the number of possible serial orders is 3! = 6.
Non-serial schedules are all schedules that are not serial. Therefore, subtract the number of serial schedules from the total number of schedules.
Total non-serial schedules = Total schedules - Serial schedules
Substitute values: 9! / (2! * 3! * 4!) - 3! = 362880 / (2 * 6 * 24) - 6 = 362880 / 288 - 6 = 1260 - 6 = 1254.