Ivy is solving the following question:  An international Mathematics competition has participants from $$11$$ different countries. At least how many participants should there be to ensure that a minimum of $$5$$ people come from the same country?     Below is her working:  $11-1=10$  $10\times5=50$  $50+1=51$  There should be at least $51$ participants.     Is Ivy correct? If not, show the correct working and answer. 
Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle