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 ((nr) 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 nr items from a set of n items
