Problem of Combination :
On a new year day every student of a class sends a card to every other student . The postman delivers 600 cards. How many students are there in the class ?
My approach : For a group of 4 students if each student gives card to each of the student then number of such combinations are :
Let A,B,C,D are students then such combination formed :
A -> B ; A -> C ; A -> D ; B->A ; C-> A; D->A; B->C ;C ->B ; B ->D ; D->B ; C-> D ; D->C So, 12 combinations are possible. How do I use this result to find the answer of this question. Please help how to proceed.
Thanks..
Best Answer
If there are $n$ students, then each student sends $n-1$ cards. So we have the total number of cards is $n(n-1)=600$ so that $n=25$.