Model: Sometimes we need to use combinations, permutations, or the Fundamental Counting Principle to calculate n(E) and n(S). For each of the following problems, use the following process: (a) Determine S and E. (b) Calculate n(S). Is repetition allowed? Does order matter? (c) Calculate n(E). (d) Compute n(E)=n(S).

1. My bike lock is a sequence of four numbers, each from 0 to 9, with repetition allowed. What is the probability that my code starts with a 1 and ends with a 4?

2. My spouse and I take a flight where we have seats in the same row, which contains six seats. What is the probability that we are sitting next to each other?