Binomial expanision

[dense plinth]

For these questions, how would you do it, because what I would have done is write out the equation of nCr in the factorial stuff and have just done 19x18x17etc and stuff like that, is there a quicker way?

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[honest fox]

top one is 0

the denominator is r!(n-r)!, so the denominator is the same for both of them, and the numerator is just 19!, so you get (19!-19!)/9!10!=0

nC1=n, so 10c1-9c1=10-9=1

[dense plinth]

What is 0?

[honest fox]

the answer to the top one

[dense plinth]

Why is it the same, because one has a 9 and the other has a 10

[honest fox]

the numerator is always n! right

[dense plinth]

yh

[honest fox]

and the denominator is r!(n-r)!

[dense plinth]

yh

[honest fox]

so the denominator for the first one is 10!(19-10)!=10!9!

and the denominator for the second one is 9!(19-9)!=9!10!

so the denominators are the same

[dense plinth]

oh yeah im dumb

thanks

[honest fox]

nws

[dense plinth]

where do you go from there

is the answer just 0?

[honest fox]

well because the denominators are the same you can just subtract the numerators

so 19!-19!=0

[dense plinth]

why dont I get that when I put it in my calculator

[honest fox]

u must be making a mistake

it is defo 0

[dense plinth]

yeah I was lol

I got 0 now

thanks for your help

[honest fox]

this is last one aswell

[dense plinth]

tysn

[honest fox]

factorials cancel nicely

say 9!/7!=9x8x7!/7!=9x8

thats how you cancel them

[dense plinth]

hold up

waht happened to the 2!

[honest fox]

i cancelled it with the 3!

3!=3x2!

and then cancel the 2!s, gives you 3

[dense plinth]

ah okk thanks for your help