Find the remainder when 11!+9! (999*8!) is divided by 18*7!-14*6! (2*8!) ?

Question

ganeshie8 · Answer

usually the answer is 0 for these type of questions

ganeshie8 · Answer

First, notice that the given expression is divisible by 8!

ganeshie8 · Answer

11!+9! (999*8!) 

= 8!(9*10*11 + 9!*999)

anonymous · Answer

I the solution it's given the ans to be   1*8! = 8!

ganeshie8 · Answer

we can factor out a "2" too : 

 11!+9! (999*8!) 

= 8!(9*10*11 + 9!*999)

= 2*8!(9*5*11 + (9!/2)*999)

anonymous · Answer

in the*

anonymous · Answer

@ganeshie8  Yes i under stand that, 8! and 8! in the num and Denominator cancells out. and remaining is 999/2

anonymous · Answer

But in the solution it's given   1*8! and the book i am referring is never wrong, its a standard book

ganeshie8 · Answer

Looks I have misinterpreted the problem, one sec..

anonymous · Answer

@ganeshie8  Let me post  a screenshot

ganeshie8 · Answer

that would help, thank you :)

anonymous · Answer

attachment

anonymous · Answer

@ganeshie8  Here it is

anonymous · Answer

@ganeshie8  Any Clue's ?

ganeshie8 · Answer

Ahh this should be easy..

ganeshie8 · Answer

11!+9!

8!(999)

8!(998+1)

8!*998 + 8!*1

8!*2*499 + 8!

ganeshie8 · Answer

Notice that 8!*2*499 is divisible by 8!*2

therefore the remainder is just 8!

anonymous · Answer

@ganeshie8   (8!*2*499+8!) / (2*8!)

anonymous · Answer

8!*2*499 is divisible by 8!*2 , buy here 8! and 8! are getting cancelled and also the 2, left one is 499

anonymous · Answer

@ganeshie8  Please make me understand.

ganeshie8 · Answer

Hey! tag me once you're online... I'd like to help you understand how these work :)