Given $$ \[\left( 102 \right)5\]
\[102\] can be communicated as the total or contrast of two numbers.
now we use binomial theorem,
The given inquiry can be composed as \[102\text{ }=\text{ }100\text{ }+\text{ }2\]
\[\left( 102 \right)5\text{ }=\text{ }\left( 100\text{ }+\text{ }2 \right)5\]
\[=\text{ }5C0\text{ }\left( 100 \right)5\text{ }+\text{ }5C1\text{ }\left( 100 \right)4\text{ }\left( 2 \right)\text{ }+\text{ }5C2\text{ }\left( 100 \right)3\text{ }\left( 2 \right)2\text{ }+\text{ }5C3\text{ }\left( 100 \right)2\text{ }\left( 2 \right)3\text{ }+\text{ }5C4\text{ }\left( 100 \right)\text{ }\left( 2 \right)4\text{ }+\text{ }5C5\text{ }\left( 2 \right)5\]
or,
\[=\text{ }\left( 100 \right)5\text{ }+\text{ }5\text{ }\left( 100 \right)4\text{ }\left( 2 \right)\text{ }+\text{ }10\text{ }\left( 100 \right)3\text{ }\left( 2 \right)2\text{ }+\text{ }5\text{ }\left( 100 \right)\text{ }\left( 2 \right)3\text{ }+\text{ }5\text{ }\left( 100 \right)\text{ }\left( 2 \right)4\text{ }+\text{ }\left( 2 \right)5\]
\[=\text{ }11040808032\]