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

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TestHub · Accepted Answer

Let n be the number of students. Now number of ways in which two students can be selected out of n students is $^{n} C_{2}$ .

∴ number of pairs of students $=^{n} C_{2}$

But for each pair of students, number of cards sent is (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 $^{n} C_{2}$ pairs, number of cards sent $= 2.^{n} C_{2}$ .

According to the question, $2 .^{n} C_{2} = 600$ 2. $\frac{n ( n - 1 )}{2 !} = 600$

or $n^{2} - n - 600 - 0$ Or, $(n - 25) (n + 24) = 0 ∴ n = 25, - 24$

But $n \neq = - 24 ∴ n = 25$

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