Number of binary sequences with no consecutive ones.

First we give each child a biscuit so that $k-n$ biscuits are over.

Then with stars and bars we find $$\binom{k-n+(n-1)}{n-1}=\binom{k-1}{n-1}$$possibilities.

HINT:

You should start by giving every child a biscuit first so that condition is solved. Further think about how many biscuits are left and in how many ways can you distribute these among the $n$ children.

Hope this helps :)

For these type of problems generating functions can also be a good approach. But in this case I would consider it an overshoot.