Poling has 8 different jobs to distribute among her 3 assistants. Each assistant will have at least two jobs to do. How many ways can Polina do this?

Answer 1

This problem can be broken up into 3 parts.

Part 1: Chose 3 jobs from the 8 and then arrange the jobs among the 3 workers.

This can be done in 8!/5! ( the binomial coefficient * 3! or ₈P₃.

Part 2: Choose 3 jobs from the remaining 5 and then arrange them as before.

This can be done in ₅P₃ ways.

Part 3: The 2 remaining jobs can be distributed in 3 ways.

Now multiply the 3 results to get 8! * 3/2!