N2004 P2 Q4

A rectangular shed, with a door at each end, contains ten fixed concret bases marked \(A\), \(B\), \(C\), … \(J\). Five on each side (see diagram). Ten canisters, each containing a different chemical, are placed with one canister on each base. In how many different ways can the canisters be placed on the bases?[1]

Find the number of ways in which the canisters can be placed

1. if \(2\) particular canisters must not be placed on any of the \(4\) bases \(A\), \(E\), \(F\) and \(J\) next to a door,

   [3]

2. if \(2\) particular canisters must not be placed next to each other on the same side of the shed.

   [3]