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

Question

Infinity Learn · 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  $$nC2$$.∴ 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 $$=$$ $$25$$.

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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