Problem 2: Auditoriums are often designed so that are fewer seats per row for rows closer to the stage. Suppose you are sitting in row 18 in an auditorium and notice that there are 73 seats in your row. It appears the row in front of you has 70 seats and the row behind you has 76 seats. Suppose this pattern continues throughout the auditorium. a) How many seats are in the first row? b) How many seats are in the 30th row? c) Write an explicit formula for the sequence where a, is the number of seats in the n" row. th

At a carnival, an individual can win a prize by choosing a rubber duck from a pond with "Win" written on the underside of the duck. There are a total of eight ducks with "Win" written on the underside of the duck, and there are 17 ducks with "Lose" written on the underside of the duck. After each pick, if a prize is won, the duck is replaced in the pond. If a prize is not won, then the duck is again placed back into the pond. If an individual makes four picks, what is the probability the individual will win a prize exactly one time? (4) (0.32) (0.68) 1! 4! (0.32)¹ (0.68)³ O2(0.32)(0.68) (0.32) (0.68)³

With a short time remaining in the day, a delivery driver has time to make deliveries to 6 different locations among the 7 locations remaining. How many different routes are possible?

Problem 2  A plethora of pigeons and a dearth of holes. i) A child places 0 or more pennies in her piggy bank each day, for 15 consecutive days. She then cracks open the piggy bank and finds that she has accumulated one dollar. (1 dollar = 100 pennies.) Explain how we know that on at least two days she placed the same number of pennies in her piggy bank. ii) Five friends are at a party. Show that at least two people shook the same number of hands.