Kenneth Rosen Edition 7 Exercise 6.2 Question 17 (Page No. 405)

Question

A company stores products in a warehouse. Storage bins in this warehouse are specified by their aisle, location in the aisle, and shelf. There are $50$ aisles, $85$ horizontal locations in each aisle, and $5$ shelves throughout the warehouse. What is the least number of products the company can have so that at least two products must be stored in the same bin?

Answer 1

50 * 85 * 5 = 21250

So there are 21250 locations where things could be stored.

All you need is 21251(21250 +1) items, and something has to share means Any fewer than 21251 items allows each item to have its own bin, so if we have 21,251 items, the 21,251st item must share a bin with another item.

ans should be 21251.