Permutation and combination?

　
a) two particular people must always be separated
The number of ways
= 8! * P(9,2)
= 2903040

Suppose A, B, C, D, E, F, G, H, I, J are the 10 people and A, B are the two particular people
| _ | _ | _ | _ | _ | _ | _ | _ |
A,B are arranged in | , | , | , | , | , | , | , | , | that is P(9,2)
C, D, E, F, G, H, I, J are arranged in _ , _ , _ , _ , _ , _ , _ , _ that is 8!


b) two of three particular people must be separated
The number of ways
= 7! * P(8,3)
= 1693440

Suppose A, B, C, D, E, F, G, H, I, J are the 10 people and A, B, C are the two particular people
| _ | _ | _ | _ | _ | _ | _ | _ |
A,B, C are arranged in | , | , | , | , | , | , | , | that is P(8,3)
D, E, F, G, H, I, J are arranged in _ , _ , _ , _ , _ , _ , _ that is 7!