2018 NJC MYE P2 Q5

A game is played with a number of cards each which has single letter printed on it. A player has ten cards, which are lettered \(A,C,E,E,E,F,L,L,W\) and \(X\) respectively.

1. A code is any arrangement of theses ten letters, for example, \(LXCELWFEEA\).
   1. Find the total number of different codes that the player can make.[1]
   2. Find the number of codes which begin and end with \(E\) and in which the two letters \(L\) are consecutive.[2]
   3. Find the number of codes such that the letter \(L\)’s are separated by at least two of the remaining letters.[3]
2. A second player chooses three of the first player’s ten cards at random, and takes them from the first player. Calculate the probability that
   1. the three cards chosen will all carry the letter \(E\) or \(L\),[2]
   2. the first player’s remaining seven cards will all carry different letters.[2]