I am just confused about part C. An explanation and a solution would be a lot he

Question

I am just confused about part C. An explanation and a solution would be a lot helpful. Thank you in advance. ( if you are not sure about the answer, please DO NOT try to answer)

For a final project of my graduate course I have to split my 20 students into 5

teams of 4.

a) How many ways do I have to form the teams?

b) Additionally, since each project requires a student to be the modeler, one student to be the reporter, one

student to solve the models, and one student to do outreach activities. How many total ways could these

teams be formed, assuming that students have already been assigned to the teams?

c) What would change in your analyses, if you consider the problem as a sequence of steps? (Note, assign

students, and then assign the roles)

Explanation / Answer

we have to form the team first and then assign roles

ways of forming a team of 4 = 20C4x16C4x12C4x8C4x4C4 {selecting 4 students out of 20 then selecting 4 out of remaining 16 and so on}

ways of assigning the roles for each team = 4C1x3C1x2C1x1C1 {1 student to be assigned out of 4 roles and then 1 student to be assigned out of 3 roles and so on}

ways of assigning the roles for 5 teams = 5x(4C1x3C1x2C1x1C1)

hence total ways = 20C4x4C1x3C1x2C1x1C1x16C4x4C1x3C1x2C1x1C1x12C4x4C1x3C1x2C1x1C1x8C4x4C1x3C1x2C1x1C1x4C4x4C1x3C1x2C1x1C1

or,

20C4x16C4x12C4x8C4x4C4x5x(4C1x3C1x2C1x1C1)

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