1. ## Factorials - adding and subtracting

Hey,
Kinda struggling with Factorials, more precisely the process of adding and subtracting them. The question is 5! + 4!. Now, the back of the book says the answer is 6x4!, I just don't understand how you reach that conclusion, can anyone help me out?

Thanks

2. Originally Posted by scott.b89
Hey,
Kinda struggling with Factorials, more precisely the process of adding and subtracting them. The question is 5! + 4!. Now, the back of the book says the answer is 6x4!, I just don't understand how you reach that conclusion, can anyone help me out?

Thanks
Hello

Recall what a factorial is. When you take the factorial of a number, you take that number and multiply it by all the numbers preceding it.

For example, $10!=10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\c dot2\cdot1$

When you add $5!+4!$, we see that this is the same as $\left[5\cdot4\cdot3\cdot2\cdot1\right]+\left[4\cdot3\cdot2\cdot1\right]$.

Looking at this closely, we notice that each term has a common factor:

$\left[5\cdot{\color{red}4\cdot3\cdot2\cdot1}\right]+\left[{\color{red}4\cdot3\cdot2\cdot1}\right]$.

So pull out the term $4\cdot3\cdot2\cdot1$, and we are left with $\left(5+1\right)\cdot4\cdot3\cdot2\cdot1=6\cdot4\c dot3\cdot2\cdot1$.

But $4\cdot3\cdot2\cdot1=4!$, so our answer is $\color{red}\boxed{6\cdot4!}$

Does this make sense?

--Chris

3. Thanks a lot, checked out the avatars on your page to. They're really good xD

Thanks again

,
,
,

,

,

,

,

,

,

,

,

,

,

,

# subtract of factorial

Click on a term to search for related topics.