how many ways are there to assign 20 different people to thr

how many ways are there to assign 20 different people to three different rooms with at least one person in each room?

Solution

20C3 - (3+3)

= 1134

arranging 20 to 3 rooms in 20C3 ways

and conditions that atleast one in a room

3 conditions for no assign for 1 room

3 conditions for no assign for 2 rooms ( assigned 20 for 1 particular room)

these 6 are removed