How do i use the pigeon hole principle for these questions?
A drawer contains 6 pairs of black, 5 pairs of white, 5 pairs of red, and 4 pairs
of green socks.
(a) How many single socks do we have to take out to make sure that we take
out two socks with the same color. (pigeonhole)
(b) How many single socks do we have to take out to make sure that we take
out two socks with diļ¬erent colors? (not really pigeonhole)
Best Answer
For a, the maximum number of different color socks is four, so if we pull five we must have a pair. The four colors are the pigeonholes.
For b, you could take out all twelve black socks first, so we have to pull thirteen to make sure we get two different.