math - gr 12
posted by joanna .
the social convenor has 12 volunteers to work at a school dance. Each dance requires 2 volunteers at the door, 4 volunteers on the floor, and 6 floaters. Joe and Jim have not volunteered before so the soicial convenor does not want to assign them to work together. In how many ways can the volunteers be assigned?
the answer is 9240, but i don't understand how to get that, help please??!
Break it up into 3 cases
1. Joe at the door, then 10 others at the door, C(10,4) on the floor, C(6,6) as floaters
= 10x210x1 = 2100
2. Joe on the floor, leaving C(10,3) for the remainder on floor, C(8,2) for the door and C(6,6) as floaters
= 120x28x1 = 3360
3. Joe as floater leaving C(10,5) for the remaining floaters, C(6,4) for the floor, and C(2,2) for the door
= 252x15x1 = 3780
total = 2100+3360+3780 = 9240