We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
146
8
avatar+581 

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?

 May 12, 2019
edited by CalculatorUser  May 12, 2019
 #1
avatar
+1

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} 

 May 13, 2019
 #2
avatar+581 
+2

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.

 May 13, 2019
 #3
avatar+4287 
+1

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.

 May 13, 2019
 #4
avatar+581 
+2

Ohhh, ok, I totally screwed up. Thanks Tertre!

CalculatorUser  May 13, 2019
 #5
avatar+4287 
+1

No problem...this is a very hard concept to grasp. I could give you a few more practice problems if you would like.

tertre  May 13, 2019
 #6
avatar+581 
+2

Yes, please, I need to understand this.

CalculatorUser  May 13, 2019
 #7
avatar+4287 
+1

1. How many positive solutions are there to w+x+y+z=60?

 

2. 6 students are running for class president out of 20 members. How many vote counts are possible, if some people decide not to vote?

 

 

After you finish these problems, I will give you new ones.

 

 

Enjoy!

 May 13, 2019
 #8
avatar
+1

Look at this somewhat similar problem on the Internet: https://www.rainbowresource.com/pdfs/products/prod060689_smp02.pdf

 May 13, 2019

4 Online Users

avatar
avatar