how many socks would you need to remove from a drawer containing 10 blue socks, 15 black socks and 5 red socks, to in sure that you have at least 2 matching socks?
You hardest time matching is if you picked one of each before you picked the second.
So, pick one blue, one black, one red, then pick one more. You have to get a matched pair in four picks.
To determine how many socks you would need to remove from the drawer to ensure that you have at least 2 matching socks, you can use the pigeonhole principle.
The pigeonhole principle states that if you have n+1 objects distributed into n pigeonholes, there must be at least one pigeonhole that contains more than one object.
In this case, let's consider each color of the socks as a pigeonhole. Since you want to ensure that you have at least 2 matching socks, you need to have at least 2 socks of the same color.
Let's go through the distribution:
1. If you remove only 1 sock, it is possible that you have one sock of each color (blue, black, and red). Therefore, you haven't guaranteed 2 matching socks.
2. If you remove 2 socks, it is still possible to have one sock of each color.
3. When you remove the 3rd sock, you have to have a sock of a previously collected color since there are only 3 colors. It could be either a blue, black, or red sock.
Therefore, you need to remove at least 3 socks to ensure that you have at least 2 matching socks.
Note: This explanation assumes that the socks are randomly distributed and does not consider the possibility of any additional socks of the same color being in the drawer.