There are 21 red, 22 yellow and 27 green socks in a drawer. How many minimum socks you must pull out at random to be sure you have at least two of each colour?
Answers
Answer:
2
Explanation:
Answer will be 3.
There are two type of socks. Also socks are not left/right footed. So we can say that all socks of one type are identical. So if you take 3 socks out you will have 3 possibilities.
Possibility 1: You have all three socks of type 1. In this case you have a matching pair of type 1.
Possibility 2: You have all three socks of type 2. In this case you have a matching pair of type 2.
Possibility 3: You have 2 socks of type 1 and 1 of type 2 or vica versa. Again in this case also you have one pair available.
This is the case of pigeonhole principle which states " If you have n pigeonholes and n+1 pigeon and pigeons are placed in these pigeonholes then atleast one pigeonhole will have more than one pigeon.
So in our case we have 2 types of socks (pigeonholes). If we take 3 socks (pigeons), we will have one type of sock atleast 2 in number. So we have a pair.