Homework 2

Counting problems

• (Mad Hatter 11-12, 2010) The number 1221 is a numerical palindrome because it reads the same forwards and backwards. How many four digit numbers are palindromic?
• (Mad Hatter 9-10, 2010) Consider a convex body having 13 vertices. For example, a cube is convex body having 8 vertices. How many distincts triangles can be constructed by connecting three different vertices of this body?
• (Mad Hatter 11-12, 2010) Ten people are to be seated in a row with 10 seats in a movie theater. Two of the 10 people do not want to sit in either of the two end seats of this row. In how many accommodating ways can all ten people be seated?