3 Consider the set X = { 1 , 2 , 3 , 4 , 5 } and suppose you have two holes. Also suppose that you have 10 pigeons: the 2 -element subsets of X . Can you put these 10 pigeons into the two holes in a way that there is no 3 -element subset S = { a , b , c } ⊂ X for which all pigeons from S go in the same hole? Then answer the same question if X = { 1 , 2 , 3 , 4 , 5 , 6 } with 15 = C ( 6 , 2 ) pigeons.