Distributing candies with a cap

In how many ways can $10$ identical candies be distributed among $4$ children if no child may receive more than $4$ (a child may still get none)?

Show hints (2)+

Start with unrestricted stars and bars, then remove the over-cap cases.
Inclusion–exclusion: subtract "one child $\ge 5$ ", add back "two children $\ge 5$ ".

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