A roll number system uses the format: DEPT(2) + YEAR(2) + MONTH(2) + SEQUENCE(4). If sequences reset monthly and there are 25 departments offering courses in 3 different years, what is the maximum number of students per month?
750,000
750,000 is correct.
Within one month the MONTH field is fixed, so the number of distinct roll numbers depends on the department, the year and the sequence.
The SEQUENCE field has 4 digits, running from 0000 to 9999, which gives \(10^4 = 10000\) possible values for each department-year combination.
There are 25 departments and 3 years, giving \(25 \times 3 = 75\) department-year combinations.
Maximum students per month \(= 75 \times 10000 = 750000\).
Hence, at most 750,000 students can be numbered in a month. 75,000 would allow only 1,000 sequences per combination, 250,000 leaves out the three years, and 300,000 does not match any valid product of the fields.
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