Question

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?

Answer 1

Given: There Are 6 Multiple Choice Questions In An Examination.

To find: Sequences of answers are possible if the first three questions have 4 choices each and the next three have 2 each.

Method: Permutation A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. Common mathematical problems involve choosing only several items from a set of items in a certain order.

Step 1: Compute the sequences of answers that are possible if the first three questions have 4 choices each and the next three have 2 each.

Only one of the four answers to the first three questions is correct. As a result, there are four possible responses.
Total number of ways to answer the first 3 questions

$\begin{array}{rcl}& =& 4{\mathrm{C}}_1\times 4{\mathrm{C}}_1\times 4{\mathrm{C}}_1\\ & =& 4\times 4\times 4\\ & =& 64\end{array}$

Each of the next three questions has two possible answers.

Total number of ways to answer the next 3 questions

$$\begin{gathered} =2{\mathrm{C}}_1\times 2{\mathrm{C}}_1\times 2{\mathrm{C}}_1 \\ =2\times 2\times 2 \\ =8 \end{gathered}$$

As a result, the total number of possible outcomes is $64\times 8=512$

Therefore, 512 sequences of answers are possible. If the first three questions have four choices each and the next three have two each.