Please help

1. Consider an experiment involving a random arrangement of the letters of the word LEXICOGRAPHY. a. Determine the cardinality of the sample space S, i.e., the number of possible arrangements of the letters of the word LEXICOGRAPHY. Define the random variable B to be the number of vowels in the first six (6) letters of the random arrangement of the letters of the word LEXICOGRAPHY. b. What are the possible values of B? Determine the probability mass function of the random variable B. Your solution must be consistent with the sample space in part (a). Show complete solutions for the PMF, following the set standard indicated in the instructions written above. Express your final answer in a table and using the fractions. c. Find the mean and variance of the random variable B. [9 points]