On a new year eve, every student of a class sends a card to every other student. If the total number of cards delivered is 1980, how many students are there in the class ?

• A. 41
• B. 43
• C. 45
• D. 47

Answer: (C)

Let the total number of students be n. For each pair, two cards are sent and the total number of pairs can be nC2 So, total cards = 2 x nC2 or 2 x nC2 = 1980,= 2 x n(n-1)/21 = 1980∴ n² - n = 1980or n² - 45n + 44n - 1980 = 0or n(n - 45) + 44(n - 45) = 0or (n + 44) (x - 45) = 0∴ n = 45, - 44 (Now, discard - value)∴ n = 45