There are 20 students on the school's student council. A special homecoming dance committee is to be formed by randomly selecting 6 students from student council. How many possible committees can be formed?

a) 720
b) 38,760
c) 27,907,200

Question

There are 20 students on the school's student council. A special homecoming dance committee is to be formed by randomly selecting 6 students from student council. How many possible committees can be formed?


a) 720
b) 38,760
c) 27,907,200

lgbasallote · Answer

use this formula:
$$\huge \frac{n!}{(n-r)!}$$
$$\huge \implies \frac{20!}{(20-6)!}$$
got it?

anonymous · Answer

I'm confused

lgbasallote · Answer

where?

anonymous · Answer

the whole thing.

lgbasallote · Answer

you have 20 students...that's why you have 20!

6 students are picked out of 20...that's why you get (20-6)!

anonymous · Answer

@lgbasallote, I believe this is a combination question.

anonymous · Answer

The order in which the students are chosen does not matter. So (a,b,c,d,e,f) is the same as (d,c,f,e,a,b).

lgbasallote · Answer

so it's $\frac{n!}{r!(n-r)!}$?

anonymous · Answer

@ashleys, you should use the formula 
$$C(n,m)=\frac{n!}{m!(n-m)!}.$$

lgbasallote · Answer

hmm okay..i get confused in these things...add a 6! there..the formula is $$\Huge \frac{n!}{r!(n-r)!}$$ therefore you have $$\Huge \implies \frac{20!}{6!(20-6)!}$$

anonymous · Answer

I also get confused by these. I'm reading a post on them now.

anonymous · Answer

@ashleys, here is a really good post related to the last 6 or so questions you've posted: http://betterexplained.com/articles/easy-permutations-and-combinations/