In how many ways can the miner tunnel from the top left box to the bottom right box of a $4 \times 4$ grid? A miner is digging a tunnel in a $4$ by $4$ grid. He starts at the top left box and can tunnel only directly down or directly towards his right.  In how many diffrent ways can he reach the bottom right box?

Hint: Let $r$ be the number of steps the miner takes to the right and $d$ the number of steps down, before reaching the bottom right of the box. 
Then $r$ and $d$ will always be equal to $3$. So this problem boils down to find the total number of sequences with length $6$ containing $3$ r's and $3$ d's.
For instance $rrrddd$ is one such sequence. 
