This problem is for "Stochastic Models" Class:

Suppose there are 10 students in the class STA 4821, say P_1, P_2, .., P_10. The instructor randomly permutes these students in a line. Let X denote who is at the front of the line. i.e. X = i means the student P_i is at the front. Let ohm be the sample space that contains all the permutations. Then answer the following: What is the size (cardinality) of ohm, e.g., |Ohm|? Describe the sets in the mathematical way for each X = i, i = 1 ~ 10. What are their sizes (cardinalities)