# Math Help - Combinations

1. ## Combinations

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

Attempt:

1) No idea. The way I did it seemed to be for permutations. 21x21x5x5x5x5

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

22 people, 1 president , then there's 21. Choose a vice president. Now 20, and 2 people lef.t

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

2. Hello, Johnboe!

1) How many 6-letter subsets can you make if 2 are consonants and 4 are vowels"

The problem is not clearly stated.

It says subsets, so the order of the letters is not considered.

If letters may not be repeated in the subsets,
. . there are: . ${21\choose2}$ choices for the consonants
. . and ${5\choose4}$ choices for the vowels.

There are: . $210\cdot5 \:=\:1050$ possible subsets.

If letters may be repeated, it is a very messy problem . . .

3. Originally Posted by Soroban
Hello, Johnboe!

The problem is not clearly stated.

It says subsets, so the order of the letters is not considered.

If letters may not be repeated in the subsets,
. . there are: . ${21\choose2}$ choices for the consonants
. . and ${5\choose4}$ choices for the vowels.

There are: . $210\cdot5 \:=\:1050$ possible subsets.

If letters may be repeated, it is a very messy problem . . .

Thank you, that is how the answer should be. How is my number 2?

4. Hello Johnboe
Originally Posted by Johnboe
Thank you, that is how the answer should be. How is my number 2?
Looks fine to me!