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# Explain Why

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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?

Aug 7, 2018

#1
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Let m represent the mailboxes and p the postcards: .

Aug 7, 2018
#2
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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 $$PC_1 \times PC_2$$ :

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

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

$$\begin{array}{|rcll|} \hline PC_1 \times PC_2 &=& \{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3) \} \\ \hline \end{array}$$ Aug 7, 2018
edited by heureka  Aug 7, 2018
#3
+1

Well The 2 postcards can go into the mailboxes like this

(1,3) (2,1) (1,2) ( 2,3) ( 3,2) ( 3,1) (1,1) (2,2)(3,3)

Aug 14, 2018