Question

There are 6 multiple choice questions on an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next 3 have 5 each?

• A. 6000
• B. 5000
• C. 4000
• D. 8000
• E. None of these

Answer 1

The correct option is D 8000

Each of the first 3 questions can be answered in 4 ways.
Each of the last 3 questions can be answered in 5 ways.
$\therefore$ By the fundamental principle of counting, sequences of answers are $4\times 4\times 4\times 5\times 5\times 5-64\times 125=8000.$