DOCUMENT(); # This should be the first executable line in the problem.
loadMacros(
"PG.pl",
"PGML.pl",
"MathObjects.pl",
"PGcourse.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGgraphmacros.pl",
"PGnumericalmacros.pl",
"PGstatisticsmacros.pl",
"contextArbitraryString.pl",
"contextIntegerFunctions.pl" # combinatoric functions like C,P
);
TEXT(beginproblem());
$showPartialCorrectAnswers = 1;
Context()->flags->set( tolerance => 0.01, tolType => "absolute");
BEGIN_PGML
Standard automobile license plates in Pennsylvania have 1 nonzero digit, followed by 3 letters, followed by 4 digits. How many different standard plates are possible in this system? [___________________]{Compute("9*26^3*10^4")}
END_PGML
BEGIN_PGML_SOLUTION
There are only 9 possibilities for the ﬁrst number since a 0 is not allowed.
Then, there are 26 possibilities for each letter, and 10 choices for the rest
of the numbers. Thus, the total number of different standard plates is [`9 \cdot 26^3 \cdot 10^4`]
END_PGML_SOLUTION
ENDDOCUMENT();