I don't get how to do these Factorials?!?

Question

8!4!
____ <-- That's the fraction bar
5!2!

... Please explain??

Answer 1

Any number followed by a ! means that you multiply by all the integers from 1 to that number. For example, 5! is 1*2*3*4*5, or 120.

Dividing factorials by one another can be done either by brute force (use a calculator for each one then plug in the numbers in the calculator again) but you can simplify it a bunch using a nifty trick. For example, 6!/4! is (1*2*3*4*5*6)/(1*2*3*4) but if you look all the numbers except for the last two in the numerator are cancelled out in the denominator. So that simplifies to 5*6, or 30.

Looking at your problem...

--- (8! 4!)/(5! 2!)

...we can rewrite this as

--- 8!/2! * 4!/5!

Now you can simplify for both, leaving all the numbers from 3 through 8 on the left side and the 5 on the bottom on the right side.

--- (3*4*5*6*7*8)/5

Cancel out the 5 on the numerator and denominator

--- 3*4*6*7*8

and if you wish you can then plug this into the calculator...

--- 4032

Answer 2

Remember that factorials are simply a whole number multiplied by all smaller whole numbers, so 8! = 8x7x6x5x4x3x2x1

Take a look at your problem: since all you're doing is multiplying and dividing factorials, you can simplify them pretty easily.

Since 5! is the same as 5x4x3x2x1, and you've already got that as part of 8!, you can simply cross 5! off and reduce 8! to 8x7x6. Same trick works for 2! (which, being 2x1 is the same thing as just writing "2") -- there's a 2 in 4!, so you can cross off the 2! and reduce 4! to 4x3. So now all you have is the numerator, which is 8x7x6x4x3 = 4032.

I suppose the other way you could do it is the long way, which is to multiply everything out and then divide the whole numbers you end up with, which would be 967,680 / 240

Answer 3

Well, I assume that you know the definition of a factorial.
Let's simplify the first part of the fraction: 8! / 5!
8! = 1x2x3x4x5x6x7x8
and
5! = 1x2x3x4x5
Numbers 1 to 5 cancel each other. This means that
8!/5! = 6x7x8
Now do the same for the rest of the fraction ( 4!/2! ) and you're done!

PS:augmom, I didn't copy from you ! We just think the same way ;-)

Answer 4

A factorial is a number multiplied by every integer less than it. SO 6! is:

6!=6*5*4*3*2*1

From this we can seet that 6! can just be represented as 5!*6, or 4!*5*6 (since 5!=5*4*3*2*1 and 4!=4*3*2*1).

You should be ably to use this information to solve your factorial problem.

Answer 5

okay , here's some help:

You know what the ! means, right? You take the number and multiply it by every integer below it. So, 4! = 4*3*2*1

So if you have 8! divided by 5!, you know they both have 5*4*3*2*1 in common, so 8!/5! just boils down to 8*7*6

Do the same with 4!/2! and your homework will be complete.

Answer 6

8! is 8*7*6*5*4*3*2*1

8! can also be written as 8*7*6*5!

So you would solve this problem in the following way:

(8!4!)/(5!2!) = (8*7*6*5!*4*3*2!)/(5!2!)
cross out like factors on top and bottom since they equal 1

(8*7*6)(4*3) is the answer

Answer 7

(8! * 4!)/(5! * 2!)

lets do it this way

8! = 8*7*6*5*4*3*2*1
4! = 4*3*2*1
5! = 5*4*3*2*1
2! = 2 * 1

(8*7*6*5*4*3*2*1 * 4*3*2*1)/(5*4*3*2*1 * 2*1)

now i am going to do it this way

(8*7*6 * 5*4*3*2*1 * 2*1 * 4*3)/(5*4*3*2*1 * 2*1)

as you can see, since you have 5*4*3*2*1 * 2*1 on top and bottom, you take take those out and you get

8*7*6 * 4*3 = 4032

ANS : 4032

Answer 8

8!4!
____ = [(8x7x6x5x4x3x2x1)(4x3x2x1)]
/{(5x4x3x2x1)(2x1)}
5!2!
8!4!
____ = [(8x7x6x4x3x1)]/{1)(1)}=4032
5!2!