
3.

How many distinct words of any
(nonzero) length can be formed using the letters of KEPLER at most once each?
(Clarification: such a word can have two Es, but can't have duplicates of any other
letter.) Words like “EREP”, “REEL”, “LEPER”,
“RE”, are some examples:


4.

David is the leader of the David
Committee. He wants to appoint 3 people to be on the Head Council. He has to choose from 9
applicants, three of which are Tommy, Jack, and Michael. In how many ways can he choose the people to
be on the Council, so that at least one of Tommy, Jack, and Michael is chosen?
