Consider the following conjecture. If p is a prime number, _aC_b and _paC_pb have the same remainder when you divide by ?. a) Show that the statement is true for _5C_2 when p=3. b) Is this statement true for _5C_2 when p=7? What is the remainder? c) How many remainders are possible when dividing by 7? What are they? d) Describe what you could do to prove the initial conjecture.
