Let n be a positive integer. Marc has 2n boxes, and in particular, he has one box filled with k apples for each k=1,2,3,…,2n. Every day, Marc opens a box and eats all the apples in it. However, if he eats strictly more than 2n+1 apples in two consecutive days, he gets stomach ache. Prove that Marc has exactly 2n distinct ways of choosing the boxes so that he eats all the apples but doesn't get stomach ache. combinatoricspermutations