There are $$5$$ white socks, $$5$$ grey socks and $$5$$ black socks in a drawer. Lina is taking out socks one at a time without looking into the drawer and wants to ensure there is at least one pair of the same colour.  She uses the following working to calculate at least how many socks she needs to take out:  Worst case scenario: I get $$1$$ white sock and $$1$$ grey sock during the first $$2$$ times.  $$\frac{\text{White}}{1}        \frac{\text{Grey}}{1}$$  The $${{3}^{\text{rd}}}$$ sock will make up one pair of the same colour.~I must get $$3$$ socks from the drawer.  Is Lina correct? If not, show the correct working and answer. 
Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems