Cancer cells are in a constant state of mutation. As they grow, they become similar but not necessarily identical to each other due to the mutations in its DNA. While some cells are sensitive to one drug, it doesn't mean that other cells are too.
Some cancer cells are naturally resistant to some of the drugs given in the course of a chemotherapy, if they are allowed to multiply, it becomes a whole new generation of cells resistant to the drug. It's basically survival of the fittest.
This is why Chemotherapy works by giving the patient more than one drug. This is to minimise the chances of one malignant cell that's resistant to a single drug to survive and multiply. The chances of a cancer cell being resistant to multiple drugs is very very low.
This year Footsteps in the Mirror will be blogging to raise money for the Association for International Cancer Research which is a non-profit organisation that helps fund cancer research throughout the world. If you're willing to help, you can sign up on the Blogathon website and pledge your amount right here. Help make a difference, no matter how small it may be.