1. (12 points) A stamp collector has a set of 10 different stamps of different values and wants to take a picture of each subset of his collection not exceeding four stamps, i.e., pictures would show one stamp, two stamps, three stamps, or four stamps. In each picture showing two or more stamps, the stamps are in a row. Showing your work,

a. determine the maximum number of different pictures possible, when the difference between two pictures would be either in the number of stamps or in the horizontal order of the stamps. For example, if the stamp collector had just two different stamps (say A and B) of different values, he would have four pictures showing: A, B, AB, and BA.

b. Among the 3-stamp pictures, how many pictures would not present the same 3 stamps. Show your work.