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.