Question

. 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.

Answer 1

Step-by-step explanation:

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.

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