# Combinations

• Nov 22nd 2009, 07:12 PM
Johnboe
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)
• Nov 22nd 2009, 08:19 PM
Soroban
Hello, Johnboe!

Quote:

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: .$\displaystyle {21\choose2}$ choices for the consonants
. . and $\displaystyle {5\choose4}$ choices for the vowels.

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

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

• Nov 22nd 2009, 09:56 PM
Johnboe
Quote:

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: .$\displaystyle {21\choose2}$ choices for the consonants
. . and $\displaystyle {5\choose4}$ choices for the vowels.

There are: .$\displaystyle 210\cdot5 \:=\:1050$ 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?
• Nov 23rd 2009, 12:35 AM