many permutations can be formed with two types of objects with n objects of type 1 and n^2 objects of type 2 when each permutation excludes

A small island country with less than 20,000 cars has decided to reissue the license plates for its cars and has decided on the following rules for assigning numbers and letters to the license plates. Each plate will have 7 character-positions that each must be filled. The leftmost character position will hold a letter from the set {D, E, H, G, X}. The next three positions will hold integers from the set {1, 9} but none of the integers can be repeated. The rightmost three positions must be entirely from the set {I, V, X} or entirely from the set {P, Q, R}, with repetition allowed in either case. For example, a valid plate would be G 127 XXI and an invalid plate would be G 337 PQX (two rules violated). What is the maximum number of different license plates following the rules? O 270,000 O 3,645,000 194,400 136,080

Find the number of ways 66 identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile than in the second pile and fewer coins in the second pile than in the third pile.