There are 22 gloves in a drawer. 5 brown pair, 4 green pair, and 2 blue pair. If you had the reach into the drawer and it was dark, how many must you choose to ensure that you have a matching pair?

there are only 3 colors, so the 4th sock must be the same color as one of the first three.

best case 2,worst case 12

To determine the minimum number of gloves you need to choose in order to ensure you have a matching pair, you need to consider the worst-case scenario. In this case, it means you want to minimize the number of gloves you choose without getting a matching pair.

To do this, let's consider the scenario where you choose gloves from each color in the drawer, but not enough to form a pair.

In the drawer, there are 5 brown pair, 4 green pair, and 2 blue pair of gloves. To ensure you don't have a matching pair, you can choose one glove from each pair.

Choosing one glove from each of the 5 brown pairs will give you 5 different gloves, as will choosing one glove from each of the 4 green pairs. So, you have chosen a total of 5 + 4 = 9 gloves.

Now, if you choose another glove, there are two possible cases:

1. If the glove you choose is blue, you already have 9 gloves (from the previous choices) that are all different from each other. So, the 10th glove you choose will definitely form a matching pair with one of the gloves you previously chose.

2. If the glove you choose is either a brown or green glove, you will have chosen one glove from each pair, resulting in 5 brown gloves, 4 green gloves, and 1 blue glove. In this case, the next glove you choose will definitely form a matching pair with one of the gloves you previously chose.

Therefore, to ensure that you have a matching pair, you must choose a minimum of 10 gloves.