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 choices each?
The first three questions have 4 choices each.
$\therefore$ $\;$ Each of the first three questions can be answered in $4$ ways each.
$\therefore$ $\;$ The first three questions can be answered in a total of $4 \times 4 \times 4 = 64$ ways.
The next three questions have 2 choices each.
$\therefore$ $\;$ Each of these questions can be answered in $2$ ways each.
$\therefore$ $\;$ The next three questions can be answered in a total of $2 \times 2 \times 2 = 8$ ways.
$\therefore$ $\;$ The total number of ways the 6 multiple choice questions can be answered $= 64 \times 8 = 512$ ways.