Find answers to your questions and expand your knowledge with IDNLearn.com. Discover detailed answers to your questions with our extensive database of expert knowledge.

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.

Sagot :

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:

[tex]\begin{gathered} \text{For thr}ee\text{ }letters\text{ }followed\text{ }by\text{ four numbers:} \\ =\text{ l}etters\times\text{ l}etters\times\text{ l}etters\times\text{numbers}\times\text{numbers}\times\text{numbers}\times\text{numbers} \\ possible\text{ number of plates }=\text{ 26 }\times26\text{ }\times\text{ 26 }\times\text{ 10 }\times10\text{ }\times\text{ 10 }\times\text{ 10} \\ =\text{ 175760000} \end{gathered}[/tex][tex]\begin{gathered} \text{For thre}e\text{ numbers followed by four letters:} \\ =\text{ numbers}\times\text{numbers}\times\text{numbers}\times\text{letters}\times\text{letters}\times\text{letters}\times\text{letters} \\ \text{possible plate numbers = 10 }\times\text{ 10 }\times\text{ 10 }\times\text{ 26 }\times26\text{ }\times\text{ 26 }\times26 \\ =\text{ }456976000 \end{gathered}[/tex]

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