Problem 4. (3 points each) Pigeonhole principle applications. Be sure to justify your answers. 4(a) A store places an order to a supplier for 5 different types of shirts. The shirts are sold in bulk, so an unknown quantity of each type is shipped when ordering. How many shirts must be ordered to guarantee the store receives at least 200 shirts of the same style? 4(b) There are 121.4 million people in the United States who earn an annual income that is at least $10,000 and less than $1,000,000. Annual income is rounded to the nearest dollar. Show that there are 123 people who earn the same a 4(c) Suppose a set of 10 numbual income in dollars. MES numbers must sum to 19. s are selected from the set (1, 2,..., 17, 18). Show that two of the selected 4(d). There are 11 2-digit numbers in a list (duplicates are allowed). Can you conclude that there are two distinct sublists of the 11 numbers that have the same sum? 2019