A university uses a roll number system: COLLEGE(3) + YEAR(2) + STREAM(2) + SERIAL(4). If there are 150 colleges, 5 years of courses, 25 streams, how many students can be uniquely identified?
18,75,00,000
A roll number is unique when its college, year, stream and serial parts together are unique, so multiply the number of choices for each part.
College: 150 choices (fits in 3 digits); year: 5 choices (fits in 2 digits); stream: 25 choices (fits in 2 digits).
Serial: 4 digits, from 0000 to 9999, which gives 10,000 different serial numbers.
Total = 150 × 5 × 25 × 10,000.
150 × 5 = 750; 750 × 25 = 18,750; 18,750 × 10,000 = 18,75,00,000.
Check: 18,75,00,000 ÷ 10,000 = 18,750 college–year–stream groups, and 18,750 ÷ 150 = 125 = 5 × 25.
Hence, 18,75,00,000.
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