Is it permissible to fast the first ten days of Dhul-Hijjah with the intention of making up for missed days of Ramadan, given that childbirth occurred on Ramadan 3rd?

It is permissible for someone who fasts the first ten days of Dhul-Hijjah to do so with the intention of making up for what they missed in Ramadan. However, it is not valid to combine the intention of making up for Ramadan and the intention of fasting the ten days in a single intention, because each act of worship is intended for its own sake.