Permutations with different numbers of objects

Hi there.

I am trying to find the number of different permutations for the following problem:

Box | | | |

Box 1 | Red | Blue | Green |

Box 2 | Red | Blue | Green |

Box 3 | Red | Blue | Green |

Box 4 | Red | Blue | Green |

Box 5 | Red | Blue | n/a |

Box 6 | Red | Blue | n/a |

Box 7 | Red | Blue | n/a |

I have seven boxes.Three of the boxes (box 5,6&7) can be either red or blue. Four of the boxes (box 1,2,3&4) can be either red, blue or green. How do I find out the number of permutations of all seven boxes?

i.e

What is the value of n?

Combination | Box 1 | Box 2 | Box 3 | Box 4 | Box 5 | Box 6 | Box 7 |

Combination 1 | R | R | R | R | R | R | R |

Combination 2 | R | R | R | R | R | R | B |

Combination 3 | R | R | R | R | R | B | R |

..... | ... | ... | ... | ... | ... | ... | ... |

Combination n | | | | | | | |

Thanks

Re: Permutations with different numbers of objects

Can you answer the following (easier, but analogous) question? I have 3 different pairs of shirts and 2 different pairs of pants. How many different outfits can I make? How can this help you answer your question?

Re: Permutations with different numbers of objects

hi,

Thanks for responding.

"I have 3 different pairs of shirts and 2 different pairs of pants. How many different outfits can I make?"

I believe that you could make 6 different outfits.

Im not sure how this helps me?

Re: Permutations with different numbers of objects

You have three choices for Box 1, 2, 3, and 4 and two choices for 5, 6, and 7. All are independent choices, therefore, it is similar to choosing outfits, just as you calculated (i.e. the product of choices).

Re: Permutations with different numbers of objects

I understand now.

So

n= (3^4)*(2^3)

= 648

If so, thanks!

Re: Permutations with different numbers of objects

Quote:

Originally Posted by

**qwertyasd** I understand now.

So

n= (3^4)*(2^3)

= 648

If so, thanks!

That's correct.