In how many ways can we distribute 6 identical pears between 3 children so that each child receives at least one pear?
I am not too sure.
I thought, 6 ways to distribute to first, 5 ways to second, 4 to third.
But that gives $120$. ??
This is a classic Stars and Bars problem, where we have $6$ indistinguishable items and $3$ distinguishable bins. Thus we have that the number of combinations is:
$$N=\binom{6-1}{3-1}=\binom{5}{2}=10$$
So there are only $10$ ways to distribute the pears such that each child has at least one pear.