6. A class contains 30 students. a. The teacher asks three questions during a cl

Question

6. A class contains 30 students. a. The teacher asks three questions during a class, which any student can answer. How many unique outcomes? b. The class is divided into 6 teams of 5 students each, numbered team #1 thru #6. Each team is to make a presentation. How many different ways can the team presentations be sequenced? C. A team of 8 students is to be selected from the class. In how many unique ways can d. Same as (c), but the 8 students are now also to be randomly seated around a circular e. The class has 15 PETE majors, 10 IE, 3 CSC majors, and 2 ME majors. If a team of 8 this team be selected? table. How many unique seatings of selected students are there? must have exactly 3 non-PETE majors on it, how many different ways can a team be formed?

Explanation / Answer

#6.
a)
first question can be answered in 30 different ways
similarly second and third can also be answered in 30 different ways.

total number of unique outcomes are 30*30*30 = 27000

b)
There are 5 teams to be sequenced
This can be done in 5! = 120 ways

c)
8 students from 30 can be selected in 30C8 ways
Hence there are 5,852,925 ways to do that

d)
if 8 students are seated around a circular table
there are (8-1)! = 7! = 5040 ways

e)
Exactly 3 non-PETE majors can be selected in 15C3 ways and remaining 5 students from 15 can be selected in 15C5 ways
Hence different ways to form a team are 15C3*15C5 = 1366365

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