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

#1**+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