Is it permissible to combine the fasting of days for making up for Ramadan and atonement, or between making up for Ramadan days and the nine days of Dhul-Hijjah?

It is not permissible to combine the fasting of expiation (kaffarah) with the fasting of make-up (qada'), because each is intended for its own sake. However, fasting to make up for missed days during the first ten days of Dhu al-Hijjah will earn both rewards.