Question

Suppose seven pairs of similar-looking boots are thrown together in a pile. What is the minimum number of individual boots that you must pick to be sure of getting a matched pair? Why?Since there are 7 pairs of boots in the pile, if at most one boot is chosen from each pair, the maximum number of boots chosen would be . It follows that if a minimum of Incorrect: Your answer is incorrect. boots are chosen, at least two must be from the same pair.

Answer 1

Answer:

We must pick at least 8 individual boots to be sure of picking at least one matching pair as explained from the pigeon hole principle.

Step-by-step explanation:

From pigeonhole principle, if k is a positive integer and k + 1 or more objects are placed into k boxes, then there is at least one box containing 2 or more objects.

Now, since we have 7 pairs of similar looking boots, thus, number of single boots we have will be;

Number of single boots = 7 x 2 = 14

Now, if we select 7 boots from the 14,then there's a possibility of selecting exactly 1 from each pair. Thus, we will not get a matching pair.

Whereas if we select 8 boots from the 14 single boots, then by the pigeon hole principle, at least 2 of the boots will need to be from the same pair. Hence we can pick at least 8 individual boots to be sure of picking at least one matching pair.