there are 7 books on a shelf , of which 2 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ?
"approach 1 at - least 1 paper back = total - no paper back 7 c 4 - 5 c 4 = 30 approach 2 at - least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back = 2 c 1 * 5 c 3 + 2 c 2 * 5 c 2 = 30 answer is a"
subtract(choose(7, 4), choose(5, 4))