In how many ways can you invite 7 friends to dinner in triplets throughout a period of 7 days so that no 3 friends are invited 2 times?
It means that for each day you invite 3 of your friends. What I thought about was to allocate one friend to all the days and another the same way so that I have to allocate friends to as little as possible places, in order to have a maximum of 2 friends invited more than 1 time. But after I did I saw that it is impossible to do so as I have invited 2 friends the maximum number of times I can and I have to allocate the 5 remaining friends in the 7 remaining places that have to be filled. Therefore at least one of the remaining has to repeated more than once. This leads me to the conclusion that this is impossible and that the question means that no 3 friends have to be repeated exactly 2 times instead of 2 times or more.
If this is the case could anyone provide me with a solution. The answer is 151 200. Any help would be greatly appreciated as this my homework for tomorrow.