Binomial Theorem Homework Help: 3/2 in Parentheses?

[g.lemaitre]

Homework Statement

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?

 

[Infinitum]

Hi g.lemaitre

Homework Statement

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?

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

3C2.

 

[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.

 

[Infinitum]

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.

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??

 

[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}

 

[SammyS]

Homework Statement

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?

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

 

[Infinitum]

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}

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

See the summary of this article : https://www.physicsforums.com/showthread.php?t=530207

 

[g.lemaitre]

thanks, i got it now.

 

[Akshay_Anti]

zero factorial equals one.