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I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(a) The candies are all different and the lunch boxes are all different?

(b) The candies are all the same and the lunch boxes are all the same?

(c) The candies are all the same and the lunch boxes are all different?

(d) The candies are all different and the lunch boxes are all the same?

(e) Exactly two of the candies are the same (but the third is different) and all of the lunch boxes are different?

Mr.Owl  Oct 22, 2017
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8+0 Answers

 #1
avatar+91027 
+2

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(a) The candies are all different and the lunch boxes are all different?

 



 

Melody  Oct 23, 2017
 #2
avatar+91027 
+2

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

 

(b) The candies are all the same and the lunch boxes are all the same?

 

The only difference is how many candies are in a lunch box

All in 1                               1

2 in 1 and 1 in another      1

all in different boxes          1

 

3 ways          

Melody  Oct 23, 2017
 #7
avatar+297 
0

I think this answer is 4  for question B, because we could have 0 candies in the boxes.

Mr.Owl  Oct 25, 2017
 #8
avatar+91027 
0

I think it is fair to assume that each candy must go into a lunch box.   :)

Melody  Oct 25, 2017
 #3
avatar+91027 
+2

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(c) The candies are all the same and the lunch boxes are all different?

 

All in 1                               4

2 in 1 and 1 in another      4*3=12

all in different boxes          4

 

4+12+4= 20 ways

Melody  Oct 23, 2017
 #4
avatar+91027 
+2

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:


(d) The candies are all different and the lunch boxes are all the same?

 

All in 1                               1

2 in 1 and 1 in another      3

all in different boxes    (one box is empty)   1     

 

5 ways 

Melody  Oct 23, 2017
 #5
avatar+91027 
+2

I have 3 pieces of candy to place in 4 lunch boxes. In how many ways can I do this if:

(e) Exactly two of the candies are the same (but the third is different) and all of the lunch boxes are different?

 

All in 1                               4ways

2 the same  in 1 box and the odd one in another   4*3=12

2 different  in 1 box and the other in another          4*3=12

all in different boxes          4C2*2 = 6*2=12ways

 

4+12+12+12 = 40ways

Melody  Oct 23, 2017
 #6
avatar+91027 
+1

These are my answers - accept them at your peril :/

You can ask questions about my logic if you want to. ....

Melody  Oct 23, 2017

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