An ant is to walk from $A$ to $B$. Calculate the number of paths. An ant has to walk from the left most lower corner to top most upper corner of $4 \times 4$ square.  However, it can take a right step or an upward step, but not necessarily in order. Calculate the number of paths.

Realise that the ant in question must take 4 steps to the right and 4 upwards. Representing a step towards right as R and an upward step as U, the ant can choose paths like RRRUUUUR, URURURUR, etc.
