SOLUTION: Find the sample space S and the corresponding size n(S) for each of the random experiments Select a letter from the word MATHEMATICS at random

This problem deserves more accurate and detailed explanation.


A sample space is the list of all possible otcomes with associated probability values for each outcome.


The given word consists of 11 letters; there are two repeating letters "M", two repeating letters "T",
two repeating letters "A", and the rest 5 letters are unique.


So, the list of all possible outcomes consists of 3 + 5 = 8 = 11 - 3  letters, but different letters go 
with different associated probabilities.


The unique letters  H, E, I, C, S have the probability    each.


The repeating letters M, T, and A go with the probability   each.


Therefore, the sample space is the list of 8 letter (without repeating), listed below with associated 
probabilities

                             M     A    T    H     E    I    C    S
    the space of events =   
                                          .