Here we see that she must also take three upsteps and five diagonal steps. Now, a step to the right or an upstep changes the parity of the coordinate sum, and a diagonal step does not change it.
So, between two right steps there must be a upstep and similarly between two upsteps there must be a right step.. We may write HVHVHV
The diagonal steps may be distributed in any fashion before, in between and after HV sequence. The required number is nothing but the number of ways of distributing 5 identical objects into 7 distinct boxes =
{11 \choose 6}.
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