High school combination question

Look at the three cases:

1) One of Joe or Jim is at the door and the other is on the floor. Then for each
of these two assignments the other 10 volunteers are arranged as follows:
1 of the 10 is assigned to the door in (10 C 1) ways;
3 of the remaining 9 are assigned to the floor in (9 C 3) ways;
the remaining 6 are floaters. This gives a total of
2*(10 C 1)*(9 C 3) ways.

2) One of Joe or Jim is at the door and the other is a floater. Then for each
of these two assignments the other 10 volunteers are arranged as follows:
1 of the 10 is assigned to the door in (10 C 1) ways;
4 of the remaining 9 are assigned to the floor in (9 C 4) ways;
the remaining 5 are floaters. This gives a total of
2*(10 C 1)*(9 C 4) ways.

3) Finally, one of Joe or Jim is on the floor and the other is a floater. Then for
each of these two assignments the other 10 volunteers are arranged as follows:
2 of the 10 are assigned to the door in (10 C 2) ways;
3 of the remaining 8 are assigned to the floor in (8 C 3) ways;
the other 5 are floaters. This gives a total of
2*(10 C 2)*(9 C 3) ways.

Thus the total number of ways the volunteers can be assigned is

2*[(10 C 1)*(9 C 3) + (10 C 1)*(9 C 4) + (10 C 2)*(8 C 3)] =

2*[10*84 + 10*126 + 45*56] = 2*4620 = 9240 ways.