A project manager is negotiating with a contractor. Neither has a good idea of how long the project will take, or how much the materials will cost?

I will go with letter A, Time and Materials because you don't know how long the project will take, we can't estimate the time and materials that will be use.

T&M - For Staff Augmentation. Ex: For Construction works, a contractor coming with required material or A software developer coming with a hired laptop. These are generally used for short term work. We pay to both men and material.

FP - Is used only when you are very clear with the work, schedules and budgets.

CPPC - Pay the invoice(s) amount for the material and also pay a certain fee (calculated in %). Ex: Invoice amount $100 and agreed percentage let us say 15%. Then we have to pay $115 ($100+15% of 100)

CPFF - Pay the invoice(s) amount for the material and also pay a certain fee (fixed). Ex: Invoice amount $100 and agreed fee let us say $8. Then we have to pay $108 ($100+8) or the invoice amount is $150, still fee remains $8.

Whereas in CPPC the fee amount varies with invoice amount.

As a buyer perspective, it is good to choose CPFF, since risk is less here to the buyer.