Farmers Alex, Ben and Charlie are discussing their plans for a piece of land which is divided into \

Question

Farmers Alex, Ben and Charlie are discussing their plans for a piece of land which is divided into $9$ plots as numbers in the diagram below.

$1$	$2$	$3$
$4$	$5$	$6$
$7$	$8$	$9$

Farmer Alex wishes to plant wheat in $2$ even-numbered plots and corn in $3$ odd-numbered plots. How many ways are there for him to do so?
A cluster is a set of $4$ adjacent plots which form a square. For example, plots $1$, $2$, $4$ and $5$ form a cluster. Farmer Ben wishes to plant $4$ different types of fruits in a cluster, each in a different plot. How many ways are there for him to do so?
Farmer Charlie wishes to select $4$ non-adjacent plots in which to plant $4$ different types of vegetables, each in a different plot. For example, plots $1$ and $2$ are adjacent, but plots $1$ and $5$ are not. How many ways are there for him to do so?

Accepted Answer

(i) $60$ (ii) $96$ (iii) $144$

\(1\)	\(2\)	\(3\)
\(4\)	\(5\)	\(6\)
\(7\)	\(8\)	\(9\)

2008 TJC P2 Q5