Homework Help: Binomial theorem

1. Jun 26, 2012

g.lemaitre

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

What am I supposed to do with the 3 over 2 in the parentheses? It can be divide and it can be take the factorial. So what do I do with it?

2. Jun 26, 2012

Infinitum

Hi g.lemaitre

It is the number of ways of choosing 2 items out of 3 different items. In other words, combinations.

3C2.

3. Jun 26, 2012

g.lemaitre

Hi Infinitum! Call me Georges.

Does that mean you take 3!/2!? That work for the 3rd and 4th term but not for the second term and for the first term I think it's undefined.

4. Jun 26, 2012

Infinitum

Okay, Georges then.

The binomial coefficient is given as,

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

Where, $0 \leq r \leq n$

Why do you think this isn't defined for the first term??

5. Jun 26, 2012

g.lemaitre

Man, infinitum, you're such a big number it takes me like forever just to count you.

I understand the binomial coefficient and can get the right answer for terms 2 3 and 4 but I'm still having trouble with the first term.

if
$$\binom{n}{r} = \frac{n!}{r!(n-r)!}$$

then

$$\binom{3}{0} = \frac{3!}{0!(3-0)!} = \frac{6}{0}$$

6. Jun 26, 2012

SammyS

Staff Emeritus
The binary coefficient, $\displaystyle \binom nk$ is defined as follows.

$\displaystyle \binom nk = \frac{n!}{k!\,(n-k)!}\ , \quad \mbox{for }\ 0\leq k\leq n$

7. Jun 26, 2012

Infinitum

0! (zero factorial) is not equal to 0....

Last edited by a moderator: May 6, 2017
8. Jun 26, 2012

g.lemaitre

thanks, i got it now.

9. Jun 27, 2012

Akshay_Anti

zero factorial equals one.