The FLDSMDFR is meant to be a new and improved version of the FLDSMDFR that will produce food items at random, but from a much larger repertoire of possible food items. Denote by r the number of potential food items to be produced by the FLDSMDFR (i.e. r is the size of its food item repertoire), which will include hot dogs, hamburgers, poutines, etc. By comparison, the regular FLDSMDFR has a food item repertoire of size 25. Assume that each time someone will push the button at the front of the new FLDSMDFR+ it will produce one of the possible food items, each item being equally likely to be produced and independent of previously produced food items. Now, the maker of the FLDSMDFR wants the number r of different possible food items to be produced by the machine to be set is such a way as to guarantee the probability of getting no hot dogs in 20 uses of the FLDSMDFR+ is at least 99%. How large does r need to be for this to be satisfied? In other words, how many different food items should the machine be able to make for the above to hold