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Answered here: https://web2.0calc.com/questions/probability_84132#r1 

This should help:

Like this:

See https://en.wikipedia.org/wiki/M%C3%B6bius_transformation

9 chocolates, 7 friends = 9 stars, 6 bars. So, there are \({15 \choose 6} = 5005 \) combinations.

If Dhruv gets 2, there are 5 chocolates for 6 people, which means there are 7 stars and 5 bars, making for \({12 \choose 5} = 792\) cases

So, the probabilty is \({792 \over 5005} = \color{brown}\boxed{72 \over 455}\) 

There are 2 stars and 10 bars which makes for \({12 \choose 10} = \color{brown}\boxed{66}\) combinations.

deleted !

I've tried that and its not right; someone please help

Double the first equation, and subtract the second equation.  Then you get 2B = 1.80, so a buger is 90 cents.

Then a soda is 2.10 - 2*90 = 30 cents.

By stars and bars, there are 5 bars and 18 stars, so there are \({23 \choose 5} = 33,649\)

But, this overcounts for the cases where x is greater than 10. 

If x is 18, there are 0 stars and 4 bars which makes for \({4 \choose 4} = 1 \) case. 

If x is 17, there are \({5 \choose 4} = 5\) cases

If x is 16, there are \({6 \choose 4} = 15\)

Notice a pattern?

This pattern will continue until \({11 \choose 4}\). Summing all these up gives us \(792\) cases.

So, there are \(33649 - 792 = \color{brown}\boxed{32,857} \) cases.

It says incorrect; thanks for trying but someone please help

Thanks, that's the right answer!

2x - 3y = -3.2 - 0.2x + 0.1y

x = 0.6x - y + 8.8

2.2x - 3.2 = 3.1y

0.4x + y = 8.8

y = 8.8 - 0.4*x

2.2x - 3.2 = 3.1(8.8 - 0.4*x)

2.3x - 3.2 = 27.28 - 1.24x

3.54x = 30.48

x = 508/59

Pluggin into y = 8.8 - 0.4*x, we get y = 8.8 - 0.4*508/49 = -3782/1475

So the solution is (508/49,  -3782/1475)

Thank you!

The number of ways is 35.