+0  
 
0
135
1
avatar

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?

Guest Jun 27, 2017
Sort: 

1+0 Answers

 #1
avatar+90127 
+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?
Say the lunch boxes are red, blue and yellow and the  candies are X,Y,Z

 

  Red Blue Green  
  XYZ 0 0 1
  0 XYZ 0 1
  0 0 XYZ 1
  XY Z or 0 Z or 0 2
  XZ     2
  YZ     2
    XY   2
    XZ   2
    YZ   2
      XZ, or YZ, or XY 6
  X or Y or Z     6
      TOTAL 27 ways

 

 

 


(b) The candies are all the same and the lunch boxes are all the same?
3 in 1 and none in the others

2 in one box and 1 in another

1 in each box

6 ways


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

  Red Blue Green  
  3 0 0 1
  0 3 0 1
  0 0 3 1
  2 1 or 0 1 or 0 2
    2   2
      2 2
  1 1 1 1
         
      TOTAL 10 ways

 

 

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

  box box Box  
  XYZ 0 0 1
  XY Z 0 1
  XZ Y 0 1
  YZ X 0 1
  X Y Z 1
         
      TOTAL 5 ways


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

 

  Red Blue Green  
  XYY 0 0 1
  0 XYY 0 1
  0 0 XYY 1
  XY Yor 0 Y or 0 2
  YY X OR 0 X OR 0 2
    XY   2
    YY   2
      XY 2
      YY 2
  X Y Y 1
  Y X Y 1
  Y Y X 1
      TOTAL 18 ways

 

That is what I get :/   My answers should be checked though :)

Melody  Jun 27, 2017

8 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details