# Determine how many groups of a given number are in a entire set

1. Jan 29, 2005

Hello all. I'm looking for an equation, one that I use to know how to figure out(but alas I am getting old and senile), that will alow me to determine how many groups of a given number are in a entire set.

For example; in a set of 5, how many possible groups of 3 would there be? The answer is 10 sets of 3 in a set of 5.

So, if anyone knows an equation for this, I would be very greatful. TIA.

James

2. Jan 29, 2005

### jamesrc

You're thinking of a combination. If I write the combination of n things taken r at a time like this: C(n,r), the formula is:

$$C(n,r) = \frac{n!}{r!(n-r)!}$$

$$C(5,3) = \frac{5!}{3!(5-3)!} = \frac{5!}{3!2!} = \frac{5\cdot 4}{2} = 10$$

3. Jan 29, 2005

### dextercioby

How about this one??$C_{5}^{3}$

Did u study combinatorics in school??

Daniel.