On a new year day every student of a class sends a card to every other student. The postman delivers 600 cards. The number of students in the class are

Let n be the number of students.Now, number of ways in which two students can be selected out of n students is  nC2.∴ number of pairs of students =nC2.But for each pair of students, number of cards sent is 2 (since if there are two students A and B, A will send a card to B and B will send a card to A).∴ For  nC2 pairs, number of cards sent =2⋅nC2.According to the question, 2⋅nC2=600or, 2⋅n(n−1)2!=600or, n2 – n – 600 = 0or, (n – 25) (n + 24) = 0∴ n = 25, –24But n ≠ –24∴ n = 25.