* probability

[squreshi]

7 teams compete in a track competition. If there are 20 events in the competition, no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?
3
4
5
6
7

I do not understand how to solve this problem. please help

[Guest]

IS THE ANS 7

[squreshi]

YES

[RA]

To minimize the number of winning teams (as required by the question) we need to maximize the events won by each team.

Number of events / Max number of events per winning team = Minimum number of teams that won

20 / 6 = 6.66

This means more than 6 teams (i.e 7) that won atleatst one event.

[imran]

I guess we can do it in much simpler way. Here it is.

we need to consider the worst scenario where in some team may not win even a single event. But the question says max one team can win is 3. so lets see.

6 * 3 = 18 : 20 - 18 = 2 ; so 6 teams can win 3 events each and the remaining two has to be won by 7th team. So the answer is 7 with atleast one win.

[esledge]

Please cite the source (author) of this problem. If no source is cited, we will have to delete the question just to be sure we are not violating someone else's copyright. Thanks!