Permutations and Combinations Practice Problems

[Draggu]

1. The problem statement, all variables and given/known

Homework Statement

1)How many six letter subsets can you make if 2 are consonants and 4 are vowels.

2) There are 22 students in the student council and 4 people are to be elected. How many ways can they be elected if:
a) there must be a vice president and president
b) vice president is excluded

Homework Equations

The Attempt at a Solution

1)
21x21x5x5x5x5

Is there a way to do this via combinations?

2a) C(22,2) * C(2,2)
b) C(22,3) * C(2,1)


These are probably horribly wrong, but I am trying. Any help would be appreciated!

 

[HallsofIvy]

1) You have not allowed for permutations of the letters chosen. IF all 6 letters are different, then there are 6! ways but you will have to allow for the same two consonants, etc.

2) First, choose a president. There are 22 ways to do that. Then choose a vice-president. There are 21 ways to do that. Finally choose 2 other members from the 20 remaining students. Permutations of the same students are not relevant.

3) Again, there are 22 ways to choose a president. Then choose 3 other members from the 21 remaining students. Permutations of the same students are not relevant.

 

[Draggu]

1) You have not allowed for permutations of the letters chosen. IF all 6 letters are different, then there are 6! ways but you will have to allow for the same two consonants, etc.

2) First, choose a president. There are 22 ways to do that. Then choose a vice-president. There are 21 ways to do that. Finally choose 2 other members from the 20 remaining students. Permutations of the same students are not relevant.

3) Again, there are 22 ways to choose a president. Then choose 3 other members from the 21 remaining students. Permutations of the same students are not relevant.

1) Not quite sure what you mean here.

2) (22,1) * (21,1) * (20,2) ?

3) (22,1) * (21,3)

 

[Draggu]

Anyone? I have a test tomorrow and am unsure :/