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@ganeshie8 uploaded

look at the 10th row in pascal's triangle :
|dw:1438086192297:dw|

We want to find \(x\) such that
\[\large ^{10}C_{x-1} - 3 *^{10}C_{x}~\gt~ 0\]

yes i m looking

|dw:1438086392992:dw|

yes >0 , understood that because sqare root function and denominator

notice that
45-3*10 > 0
10-3*1 > 0
1 - 3*0 > 0
so, x = 9, 10, 11 are fine

The answer is none of these... so I am confused

x = 8 doesn't work because
120 - 3*45 < 0
similarly x>11 doesn't work because
0 - 3*0 = 0

answer is \(a\) to my knowledge

let me analyse once, give me some time then I may ask you if you have no problem @ganeshie8

sure

Is this the language for combinations? Thats interesting.... hmmm...

#to#

\(\large ^nC_r\) is read as \(\large n~~\text{choose}~~r\)

it is called binomial coefficient and represented by symbol :
\[\large \binom{n}{r}\]

// Its for Combination

45-3*10 > 0
You checked this for 9?

yes that is for x = 9

suppose you went for shopping and liked 5 shirts

but you can only buy 3 of them

how many ways are there to choose 3 shirts from the 5 shirts ?

for definiteness, lets call the shirts : \(a,~b,~c,~d,~e\)

calculations say 10

can you list them all ?

ok go on... nice

no, I don't have that strong concept.... I would definitely understand from you.... nice....

no, just list them all, its a simple counting problem

you can buy the shirts \(a,b,c\) or \(b,c,d\) or \(c,d,e\) or ...
try listing them all

okay ...
abc acd bed
bcd ade bec
cde aeb

more two

looks two are missing yeah

I am trying :P

no no not bae

```
{a,b,c}
{a,b,d}
{a,c,d}
{b,c,d}
{a,b,e}
{a,c,e}
{b,c,e}
{a,d,e}
{b,d,e}
{c,d,e}
```

\(\large ^{5}C_3\) gives the number of ways you can choose 3 shirts from 5

##found##

yes yes.... ofcourse

I am talking about counting.. thats hard! :P

as you can see its not so pleasant to list them all... why would you want to do that lol

ofcourse it is unpleasant! but Maths is Maths.... but can you tell me how did you do it?

Can Wolfram do this?

https://jsfiddle.net/ganeshie8/r2hjr3js/1/

Thank you so much for giving your precious time.... :)

comb(n, set)
lists all the combinations of size "n" from the set "set"

ya its working.... thank you....

Ok got it! :P