8!/5!*7!/7!10!

Question

just solve it

Answer 1

8!/5!*7!/7!10!

 

You should use parenthesis to make it clear what you mean.

 

I'll assume this, where * means multiply (tell me if I'm wrong):

 

(8!/5!)*(7!/(7!*10!))

 

First replace the 7!/7! with 1/1:

 

(8!/5!)*(1/(1*10!)) =

 

(8!/5!)*(1/10!) =

 

(8!*1)/(5!*10!) =

 

8!/(5!*10*9*8!) =

 

Replace 8!/8! with 1/1:

 

1/(5!*10*9*1) =

 

1/(5*4*3*2*1*90) =

 

1/(20*6*90) =

 

1/(1800*6) =

 

1/10800

Answer 2

Hi Sam;

8!/5!*7!/7!10!

Let's begin with...

8!/5!

[(8)(7)(6)(5)(4)(3)(2)(1)]/[(5)(4)(3)(2)(1)]

The (5)(4)(3)(2)(1) is in the numerator and denominator.  It cancels...

[(8)(7)(6)(5)(4)(3)(2)(1)]/[(5)(4)(3)(2)(1)]

(8)(7)(6)

Let's move on to...

7!/7!10!

The 7! is in the numerator and denominator.  It cancels...

7!/7!10!

1/10!

[(8)(7)(6)]*[1/(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)]

[(8)(7)(6)]*[1/(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)]

1/[(10)(9)(5)(4)(3)(2)(1)]

1/10800