Question

A candy store sells 3 different flavors of soda: orange, vanilla, and root beer. An order of soda comes with 4 straw choices: paper, plastic, metal, and cardboard. How many unique ways can you order a soda with a straw? (You can only select one flavor with one type of straw.

Answer 1

LETS USE COMBINATION AS ORDER IS MANDATORY HERE

`\\ \rm\Rrightarrow ^nC_r=(n!)/(r!(n-r)!)`

`\\ \rm\Rrightarrow ^4C_3`

`\\ \rm\Rrightarrow (4!)/(3!(1!))`

`\\ \rm\Rrightarrow (4(3!))/(3!)`

`\\ \rm\Rrightarrow 4ways`

Answer 2

12

Explanation:

It is helpful to draw a sample-space diagram of all the possible outcomes:

`\large \begin{array} c \cline{1-4} & orange & vanilla & root\:beer \\\cline{1-4} paper & 1 & 1 & 1 \\\cline{1-4} plastic & 1 & 1 & 1 \\\cline{1-4} metal & 1 & 1 & 1 \\\cline{1-4} cardboard & 1 & 1 & 1 \\\cline{1-4}\end{array}`

Therefore, there are 12 possible outcomes.