• Discrete Structures
  Recall C(n,r) counts the number of ways to choose r items from a set of n, without repetition. The formula is C(n,r) = n! / ((n-r)! * r!). a) Using algebra, show that C(n+1,r+1) - C(n, r+1) = C(n,r). b) Using algebra, show that C(n, r) = C(n, n - r). c) Explain in your own words, why the identity in part b makes sense. In other words why is the number of ways to choose r items from a set of n items always the same as the number of ways to chose n-r items from a set of n items?