**In how many ways can 2 postcards be mailed into 3 mail boxes**.

The answer is 9. It's solved by doing 3^2.

Could anyone please explain why it is solved like this?

Gh0sty15
Aug 7, 2018

#2**+1 **

**In how many ways can 2 postcards be mailed into 3 mail boxes.**

**The answer is 9. It's solved by doing 3^2. **

**Could anyone please explain why it is solved like this?**

\(\text{ Let postcard $1 = PC_1$ } \\ \text{ Let postcard $2 = PC_2$ }\)

\(\text{The subset $PC_1 = $ { Box $1,\ $ Box $2,\ $ Box $3$ } } \\ \text{The subset $PC_2 = $ { Box $1,\ $ Box $2,\ $ Box $3$ } } \)

The cartesian product of the subsets is \(PC_1 \times PC_2\) :

\(\begin{array}{|rcll|} \hline && PC_1 \times PC_2 \\ &=& 3\times 3 \\ &=& 3^2 \\ &=& 9 \\ \hline \end{array}\)

\(\begin{array}{|r|c|c|c|c|} \hline & PC_2: & \text{Box}_1 & \text{Box}_2 & \text{Box}_3 \\ PC_1 & & \\ \hline \text{Box}_1 & & (1,1) & (1,2) & (1,3) \\ \text{Box}_2 & & (2,1) & (2,2) & (2,3) \\ \text{Box}_3 & & (3,1) & (3,2) & (3,3) \\ \hline \end{array} \)

\(\begin{array}{|rcll|} \hline PC_1 \times PC_2 &=& \{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3) \} \\ \hline \end{array}\)

heureka
Aug 7, 2018