(iv) Check that the formula () = 21" holds for rows n = 0 to 5...
(iv) Check that the formula () = 21" holds for rows n = 0 to 5 in Pascal's triangle. (If it doesn't work for n = 4 or 5, go back and redo (iii)!) (v) Prove the formula of (iv) using (ii). (a) using (ii); (b) by proving that both sides of the formula represent the number of subsets of a set of n elements. For the left side use the addition rule for counting after partitioning the collection of all subsets according to size. And for the right side use the product rule for counting after identifying a subset A C {1,2,...,n} with the sequence of zeros and ones which is the indicator of A.