Rackham Graduate School has 8,000 students (5,000 PhD students and 3,000 masters stu- dents). The Rackham Student Government Executive Board has 4 student members: a President, a VP of Operations, a VP of Finance, and a VP of Administration. Reminder: no need to simplify your answers in this homework (unless problem explicitly says to). a) How many ways are there to choose the Exec Board from all Rackham students?
b) How many ways are there to choose the Exec Board so that there is at least one masters student and one PhD student? (for any of the 4 positions)
c) How many ways are there to choose the Exec Board if the VP positions have to be PhD students (the president can be either a PhD or Masters student)?
d) How many ways are there to choose the Exec Board so that there is at least one masters student VP?

a) 8,000!/(8000 - 4)! ways

b) 15,000,000 + 7998!/(7998 - 2)! ways

c) 5,000 + 7,999!/(7,999- 3)! ways

d) 3,000 + 7,999!/(7,999- 3)! ways

Step-by-step explanation:

The number of students at Rackham Graduate School = 8,000 students

The number of PhD students = 5,000

The number of masters students = 3,000

The number of student members of the Rackham Student Government Executive Board = 4 students

a) The number of ways there are to choose the Exec Board from all Rackham students = The number of ways to choose 4 students from 8,000 = 8,000!/(8000 - 4)!

b) The number of ways of having one Master student in the board = 3,000 ways

The number of ways of having one PhD student in the board after selecting a masters student = 5,000 ways

The number of ways of selecting the remaining 2 members =

7998!/(7998 - 2)!

The total number of ways of selecting at least one masters and one PhD in the board is therefore equal to 5,000 × 3,000 + 7998!/(7998 - 2)! ways

c) The number of ways of choosing the VP position as PhD = 5,000 ways

The number of ways of choosing the other three members = 7,999!/(8000 - 3)!

Therefore, the total number of ways = 5,000 + 7,999!/(7,999- 3)! ways

d) The number of ways of choosing a masters student as the VP position = 3,000 ways

The number of ways of choosing the other three members = 7,999!/(8000 - 3)!

Therefore, the total number of ways = 3,000 + 7,999!/(7,999- 3)! ways

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

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step-by-step explanation: