A cube that has a volume of \(1.00 \mathrm{~m}^{3}\) contains \(N\) distinguishable particles. Determine the probability that all the particles are in a smaller volume \(V\) of the cube if

(a) \(N=1, V=0.500 \mathrm{~m}^{3}\);

(b) \(N=1, V=0.250 \mathrm{~m}^{3}\);

(c) \(N=1, V=0.0100 \mathrm{~m}^{3}\);

(d) \(N=2, V=0.500 \mathrm{~m}^{3}\); 

\((e) N=4, V=0.500 \mathrm{~m}^{3}\).