Question

# In how many ways can a 10-question true-false exam be answered? (Assume that no questions are omitted)

Probability and combinatorics
Each question can be answered in 2 ways: true of false. So by the Fundamental Counting Principle, a 10-question true-falce exam can be answered in: $$\displaystyle{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}\cdot{2}={2}^{{10}}={1024}$$ ways.