Counting and Induction

1. A kiosk at the mall offers free gift wrapping during the holiday season. They haye 5 different wrapping paper patterns {Christmas trees, snowakes, elyes, reindeer, and polka dots}, 8 different nbbon colors (silver, white, green, red, blue, yellow, gold, and pink}, and 4 different sized boxes (small, medium, large, and extra large). a) If the kiosk has 431 people stop to get a gift wrapped in one week, show that at least 4 of the gifts were wrapped in exactly the same way. b) Suppose that all of the 431 shoppers from above happened to have their gifts wrapped with either snowake wrapping paper, or a green nbbon, or a medium sized box. Knowing the following information, determine how many customers had their gift wrapped with snowake wrapping paper, and green n'bbon, and a medium sized box: 30D shoppers had snowake wrapping paper 2513 shoppers had green n'bbon 15E} shoppers had a medium box 11!]| shoppers had snowake wrapping paper and green ribbon TU shoppers had snowake mapping paper and a medium box I'D shoppers had green ribbon and a medium box