For a community service project, 10 students volunteer to do some cleaning
up at an old folk’s home. The teacher in charge wants to split them up in 3
groups. One group will consist of 5 students in clean the rooms; another
group of 3 students to clean the toilets; the last group of 2 students to
sweep the corridors. Find the number of ways the teacher in charge can form
the groups.
For the rooms, 10 students CHOOSE 5. That's 10C5 = 252 ways
For each of those 252 ways, we have for the toilets,
5 remaining students CHOOSE 3. That's 5C3 = 10 ways.
So there are 252∙10=2520 ways to choose the room crew and toilet crew
For each of those 2520 ways, we have for the corridor crew,
2 remaining students CHOOSE both 2. That's 2C2 = 1 way
Answer: 252∙10∙1 = 2520 ways the teacher can form the three groups.
Edwin