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suppose nine 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 9 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 boots are chosen, at least two must be from the same pair.



Answer :

the minimum number of individual boots that must be picked to be sure of getting a matched pair is 2.

Since there are 9 pairs of boots in the pile, we can determine that each pair has two boots. If at most one boot is chosen from each pair, the maximum number of boots chosen would be 18.

To guarantee that a matched pair of boots is chosen, we must pick at least two boots from the pile, one from each boot of the same pair. Therefore, the minimum number of individual boots that must be picked to be sure of getting a matched pair is 2.

Number of pairs of boots in the pile = 9

Number of boots in each pair = 2

Maximum number of boots that can be chosen = 9 x 2 = 18

Minimum number of boots required to guarantee a matched pair = 2

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