I can solve for how many ways there is to choose five team members from $16$ workers $= 16C5$. But, I'm having a hard time figuring how to approach the other question can anyone guide me in the right direction?
There are a total of $16$ workers made up $9$ humans and $7$ robots. There are five roles: leader, navigator, doctor, operator, and technician. Each role has to filled by a different worker. How many different crews have
1) a robot as leader?
2) exactly one robot on the crew?
3) at least one robot on the crew?
1) There are 7 ways to pick the leader and then 15x14x13x12 ways to complete the team. You must then multiply these numbers.
2) There are 7 ways to pick the robot and so the 5 roles for the robot gives 35 possibilities, There are then 9x8x7x6 ways of completing the team.
3) Find the number of teams without any robots and subtract this from the total number of teams. Over to you but ask if you are unsure of your answer.