Would like answers to both of these questions thank you If t

Would like answers to both of these questions, thank you.

If ten friends are born from 2000-2010, are at least two of the born in the same year? A company has 50 clients and seven employees assigned to them. The manager says that the most number of clients that each employee will serve is seven. Is this true? Explain your answer.

Solution

1) No this is not true. It is possible that the birth years of the ten friends are all different. For example: 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 - 10 different years within the range 2000-2010.

b) Again, this is not true. It is possible that each employee serves all of the 50 clients. If no client is served by more than 1 employee then again this is not true. For example, 6 employees can serve one client each and the 7th employee serves the remaining 50-6=44 clients.