2015 TPJC P2 Q8

A game is played with ten cards, each of which has a single letter printed on it. The ten cards consist of the following letters respectively.

A, E, L, L, L, M, P, P, U, Y

1. A code is formed by any arrangement of these ten letters. For example, AMPULLPYLE forms a code.
   1. Find the number of codes which begin and end with L and the two letters P must be next to one another.[2]
   2. Find the number of codes in which all the vowels are arranged in alphabetical order from left to right.[3]
   3. Find the number of codes in which at least two letters L are together.[3]
2. A player chooses three of the ten cards at random.
   Find the probability that the remaining seven cards left consist of all different letters.[2]