Question

There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first 2 questions have 3 choices each, the next 2 have 4 choices each and the last two have 5 choices each?

• A. 3450
• B. 3300
• C. 3600
• D. 3400
• E. None of these

Answer 1

The correct option is C 3600

First question can be answered in 3 ways.
Second question can be answered in 3 ways.
3 questions can be answered in 4 ways.
4 questions can be answered in 4 ways.
5 questions can be answered in 5 ways.
6 questions can be answered in 5 ways.
Hence, by fundamental principle of counting, the required number of sequences of answers
$=3\times 3\times 4\times 4\times 5\times 5=3600.$