Practice$22$: Problem $16$

$(1$ point$)$

This question concerns binary strings of length six. These binary strings can be divided up into four types depending on their first and last bits. Thus the types are: OXXXX$0,$ OXXXX$1,1$XXXX$0,1$XXXX$1.$

How many binary strings of length six must you select before you are sure to have at least $6$ that are of the same type? $($Assume that when you select bit strings you always select different ones from the ones you have already selected.$)$