# Factorials - adding and subtracting

• October 30th 2008, 07:54 AM
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
• October 30th 2008, 08:12 AM
Chris L T521
Quote:

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
• October 30th 2008, 12:25 PM
scott.b89
Thanks a lot, checked out the avatars on your page to. They're really good xD

Thanks again (Clapping)