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Srry im just starting alg 1

We all start there.

@ganeshie8 any ideas?

This is stars and bars problem
Consider \(n+k\) stars and \(n-1\) bars

How do we work with this?

Yes, stars and bars is just a visualization technique

13 is kinda large,
lets try a much simpler example :
\(a+b+c+d+e = 7 \)

Consider \(7\) stars and \(4\) bars :
\(\star |\star| \star \star| \star \star| \star \)

Yes, a = 1, b = 1, c = 2, d = 2, e = 1

above arrangement represents a solution :
\((1,1,2,2,1)\)

right, what about below
\(\star |\star| |\star \star \star \star| \star\)

1, 1, 0, 4, 1

I see what it represents, but it doesn't get us any closer to solving the question though, right?

How many locations are there for placing 4 bars ?

That's what we have to figure out...

Isn't it trivial to figure that out just by looking at the stars and bars ?

Ew...

lets do one more example problem

Wow, OK.

find number of nonnegative integer solutions to the equation
\(a+b+c = 5\)

you want to partition \(5\) into \(3\) parts
so consider \(5\) stars and \(2\) bars

sure, you can, thats one solution : \((0,0,0,0,7)\)

Oh, so I had to look at it as a string! Nice.

Thanks!

Am I missing something? Is that the number of nonnegative solutions too?

\(\large \star | |\star \star \star| \star \star | \star\)
two adjacent bars is not allowed

So the number of positive solutions is \(\binom{11}{4} - \binom{10}3\) ...?

\(7\) stars :
\(\star~~\star~~\star~~\star~~\star~~\star~~\star \)
where can the \(4\) bars go ?

oh nice! let me answer this

|dw:1442673808024:dw|

wait, OHHHH

|dw:1442673856670:dw|

yes, I'm stupid...

yay

so that is where the\[\binom{n-1}{k-1}\]comes from

Yep

That's great.

Do you know rotational mechanics?

yup, that's what I got too. great.

that sounds like physics ?

yeah, physics :P

uniform circular motion or something more advanced ?

oh, wait, you didn't study rotational mechanics in high-school/engineering?

never heard of that name before

torque/angular momentum/moment of inertia/angular velocity/angular acceleration