Question

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

• A. $42$
• B. $34$
• C. $25$
• D. None of these

Answer 1

Answer: (C)

$25$

Let the number of students be $n$.

Then 2 students can be selected out of n students in ${{}^{n}c}_2$ ways = number of pairs of students.

But for each pair of students, the number of cards sent is 2 (since if there are 2 students A and B, A will send a card to B and B will send a card to A)

So for ${{}^{n}c}_2$ pairs, number of cards sent will be $2\cdot {{}^{n}c}_2$

Now given that $2\cdot {{}^{n}c}_2=600$

$\Rightarrow n^2-n-600=0\Rightarrow n=25,-24$

$n$ cannot be negative so $n=25$