Assuming that in a box there are 10 black socks and 12 blue socks, calculate the maximum number of socks needed to be drawn from the box before a pair of the same color can be made. using the pigeonhole principle

Step-by-step explanation:

The pigeonhole principal states that if n items are put into m containers, with n > m then at least one container must contain more than one item.

In other words, to find the case where maximum attempts are required, we eliminate all the cases where our criterion is not met and we will be left with the desired result.

For this case, the box has 10 black socks and 12 blue socks.

10 black socks = 5 left foot ones and  5 right foot ones

12 blue socks = 6 left foot ones and 6 right foot ones

If we draw all left foot or right foot ones then we will not have a pair till 11 draws have been made.

The next socks drawn will be a right foot one of blue or black color and a pair will be made.

Therefore, the maximum number of socks needed to be drawn from the box are 12.