+2864 Use sticks and stones to solve this :
Uncle Henry is feeling generous and has decided to distribute four $1 bills, three $5 bills, two $20 bills, and a $100 bill to three nephews. How many different ways can he distribute the money?
Are the nephews, in this case, the stones? And the money the sticks?
How should I set up my combination?
Here is my naive approach:
Subsets [O, O, O, O, F, F, F, T, T, H, {3} ] =53
O=$1, F=$5, T=$20 and H=$100
{F, F, F} | {F, F, H} | {F, F, O} | {F, F, T} | {F, H, F} | {F, H, O} | {F, H, T} | {F, O, F} | {F, O, H} | {F, O, O} | {F, O, T} | {F, T, F} | {F, T, H} | {F, T, O} | {F, T, T} | {H, F, F} | {H, F, O} | {H, F, T} | {H, O, F} | {H, O, O} | {H, O, T} | {H, T, F} | {H, T, O} | {H, T, T} | {O, F, F} | {O, F, H} | {O, F, O} | {O, F, T} | {O, H, F} | {O, H, O} | {O, H, T} | {O, O, F} | {O, O, H} | {O, O, O} | {O, O, T} | {O, T, F} | {O, T, H} | {O, T, O} | {O, T, T} | {T, F, F} | {T, F, H} | {T, F, O} | {T, F, T} | {T, H, F} | {T, H, O} | {T, H, T} | {T, O, F} | {T, O, H} | {T, O, O} | {T, O, T} | {T, T, F} | {T, T, H} | {T, T, O}
+2864 Um I had an entirely different answer (probably not correct I will have to see what the answer is)
Using stars and bars
| | | Which represents nephews
O O O O F F F T T H Which represents money
So we have | | | O O O O F F F T T H
Ok so I think it is permutation.
So permutation formula
13! / (13-10)!
1716 ways???
Please, if someone is good at this, explain and check our answers.
+4622 We can split this up into multiple cases to consider.
One-dollar bills: Set up the dividers to get (7-1)C(2)=6C2=15 ways.
Five-dollar bills Again...use the same method to get (6-1)C2=5C2=10 ways.
Twenty-dollar bills: (5-1)C2=6 ways.
Hundred-dollar bills: Any three nephews can get it, so there are three ways or (4-1)C2=3C2=3 ways.
Thus, the answer is 2700 ways.
