Problem 2. What is the probability of the following events when we randomly select a permutation of the 26 lowercase letters of the English alphabet? a) The first 10 letters in the permutation are in alphabetical order? (b) "cat" are the first letters of the permutation and "dog" are the last? (c) letters "cat" are next to each other in the permutation? d) "c" and "t" are separated by at least 20 letters in the permutation? (e) "c" precedes both "a" and "t" in the permutation? Provide detailed justification for your answers