Question

A class contains 30 students.

1) The teacher asks three questions during a class, which any student can answer. How many unique outcomes?

2) 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?

3) A team of 8 students is to be selected from the class. In how many unique ways can this team be selected?

4) Same as (c), but the 8 students are now also to be randomly seated around a circular table. How many unique seatings of selected students are there?

5) The class has 15 PETE majors, 10 IE, 3 CSC majors, and 2 ME majors. If a team of 8 must have exactly 3 non-PETE majors on it, how many different ways can a team be formed?

Answer 1

1) Total number of ways = 30*30*30 =27000

2) Required no. of ways in which presentations can be sequenced = 6*5*4*3*2*1 = 720

3) Team of 8 students can be selected from 30 in 30C8 ways

4) Now, 8 students can be seated around a circular table in !(8-1) = !7 ways

Thus, total ways = 30C8 * !7

5) Since, There should be exactly 3 non-PETE majors, there should be 5 PETE majors

Thus, total no. of ways in which a team can be formed = 15C5 * (10+3+2)C3 = 15C5 * 15C3