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?

let us consider it to be a string of length $8$ with $4$ repetitions of $r,d$ so here total ways/ permutations are $\frac{8!}{4!.4!}=\frac{1680}{24}=70$ so thats all total ways are $70$ hope its clear.
