Suppose five 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 5 pairs of boots in the pile, if at most one boot is chosen from each pair, the maximum number of boots chosen would be 5. It follows that if a minimum of 6 boots are chosen, at least two must be from the same pair.

Question

02-09-2025
Mathematics

College

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Suppose five 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 5 pairs of boots in the pile, if at most one boot is chosen from each pair, the maximum number of boots chosen would be 5. It follows that if a minimum of 6 boots are chosen, at least two must be from the same pair.

Answer :

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shallomisaiah19 shallomisaiah19 · Answer 1 · 2025-05-29T12:11:57-04:00

Answer:

Step-by-step explanation:

Every pair of boots has one boot for the right leg and one for left leg ,It is given that there are 5 pairs of boots

Number of single boots = 5 x 2 = 10

Pair Number Left Leg Right Leg

1 (L) R

2 L (R)

3 L (R)

4 (L) R

5 (L) R

Now, Let us start picking the boots at random ,with at most one boot from each pair.

For example, let the first boot be the left of pair 1, the second boot be the right of pairs 2 , and so on .

Let us circle the boots that are picked in the table.

If the above rule of at most one boot from a pair is followed , we can see that we can pick 5 boots and still not get a pair.

But as soon as we choose the 6th boot from the remaining boots, it is clear that it will complete a pair

for example ,if we pick the left boot of pair 2, it will complete pair 2.

therefore,

Since there are 5 pairs of boots in the pile, if at most one boot is chosen from each pair ,the maximum number of boots chose would be 5. It follows that if a minimum of 6 boots are chosen ,at least two must be from the same pair.