An online tshirt store would like to determine if its custom

An online t-shirt store would like to determine if its customers return one of the sixteen t-shirt designs it sells when they buy two or more of them. (a) Determine the minimum number of customers needed to test all pairs of t-shirts to see if the purchases of particular pairs of t-shirts lead to more returns, assuming that each customer buys eight t-shirts.(b) If the store would like to run a market test to determine which pairs of t-shirts cause returns, how should the sixteen t-shirts be distributed among the number of customers you determined in part (a) so that all pairs of t-shirts are tested out?

Solution

Customers buy 8 t shirts out of the 16 t-shirt designs . Assuming that the 8 tshirts are all of different designs

a> we are given that each customer buys 8 t shirts and there are 16 t shirt designs

=> any 2 customers can buy 8 t shirts with the same design

but simce we need the minimum number of customers then this could happen

when the first 2 customers but 8 t shirts each and the first customer takes 8 designs and the other one takes the remaining 8 t shirt designs

=> the minimum number of customers needed to test all the 16 designs is = 2