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