Question

Texas' general issue plates currently have seven-digits that consist of three letters andfour numbers (AAA 9999) or three numbers followed by four letters (999 AAAA).Which pattern creates the most plates? Justify your answer.

Answer 1

the pattern with three numbers followed by four letters have the most plates

Ex[planation:

letters from A to Z = 26

Numbers from 0 to 9 = 10

There 7 digits plate numbers that consists of three letters:

`\begin{gathered} \text{For thr}ee\text{ }letters\text{ }followed\text{ }by\text{ four numbers:} \\ =\text{ l}etters*\text{ l}etters*\text{ l}etters*\text{numbers}*\text{numbers}*\text{numbers}*\text{numbers} \\ possible\text{ number of plates }=\text{ 26 }*26\text{ }*\text{ 26 }*\text{ 10 }*10\text{ }*\text{ 10 }*\text{ 10} \\ =\text{ 175760000} \end{gathered}`
`\begin{gathered} \text{For thre}e\text{ numbers followed by four letters:} \\ =\text{ numbers}*\text{numbers}*\text{numbers}*\text{letters}*\text{letters}*\text{letters}*\text{letters} \\ \text{possible plate numbers = 10 }*\text{ 10 }*\text{ 10 }*\text{ 26 }*26\text{ }*\text{ 26 }*26 \\ =\text{ }456976000 \end{gathered}`

The pattern with three numbers followed by four letters have a higher possible number of plates than three letters followed by four numbers.

Hence, the pattern with three numbers followed by four letters have the most plates