How many socks take from the shelf to ensure that at least 2 of them have the same colour?

Question

I'm a little unsure on how to approach this question:

A drawer shelf contains 6 pairs of socks, each pair a diff color How many socks should be taken from the shelf to ensure that at least 2 of them are of the same?

Could I use a combination for this? $C(6, 2) = 15$? Thanks in advance!

Answer 1

In the worst case, you may pick $6$ socks each of a different color. So in order to ensure that we get at least two socks on the same color, you need to pick at least $7$ socks. It's a simple application of the Pigeonhole principle.

Answer 2

Seven. Worst case: You get one of each color (six), then the seventh must match one of the others.

Answer 3

Hint: In the worst case scenario, you select from a different pair each time until you run out of pairs, then select one more sock.   Only if you select this many socks, are you guaranteed to have at least a matching pair.

Answer 4

Seven draws, from the pigeonhole principle.