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

Question

Philoid · Accepted Answer

Given: Multiple choice question, only one answer is correct of the given options.

So, for the first three questions only one answer is correct out of four, similarly, for the remaining three question, only one answer is correct out of two.

Number of outcomes possible is ⁴C₁ × ⁴C₁ × ⁴C₁ for the first three and ²C_{1 ×} ²C₁ × ²C₁ for the remaining three.

Hence, total possible outcomes possible are ⁴C₁ × ⁴C₁ × ⁴C₁ × ²C_{1 ×} ²C₁ × ²C₁ = 512