1. ## Evaluation

What formula is used for this problem?

Evaluate
20!
18!

2. Originally Posted by mike1
What formula is used for this problem?

Evaluate
20!
18!
The "!" denotes the factorial of the number preceeding it. It is the product of
all the integers less than the number and greater than 1. By convention we take 0!=1.

So:

20!= 1x2x3x4x5...x18x19x20

18!= 1x2x3x4x5...x18.

So:

20!/18!=(1x2x3x4x5...x18x19x20)/(1x2x3x4x5...x18)=19x20=380

RonL

3. Originally Posted by mike1
What formula is used for this problem?

Evaluate
20!
18!
Hello, Mike,

use the definition:

$\frac{20!}{18!}=\frac{1 \cdot 2 \cdot 3 \cdot ... \cdot 18 \cdot 19 \cdot 20}{1 \cdot 2 \cdot 3 \cdot ... \cdot 18}$

Cancel equal factors and you'll get: 19 * 20 = 380

EB

4. So, what is the difference then if there isn't an ! and it is just to evalute:

Evaluate
{11}
{ 3}

5. Originally Posted by mike1
So, what is the difference then if there isn't an ! and it is just to evalute:

Evaluate
{11}
{ 3}
Well this is ambiguous there are plenty of possible meanings for this, but
I will assume you mean the binomial coefficient or combinations symbol:

${11 \choose 3}$

also written:

$C^n_k$

This is defined to be:

${n \choose k}=\frac{n!}{k!\,(n-k)!}$,

so in this case we have:

${11 \choose 3}=\frac{11!}{3!\,8!}=\frac{11 \times 10\times 9}{3 \times 2 \times 1}=165$,

RonL