# Thread: Permutations with different numbers of objects

1. ## 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

2. ## 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?

3. ## 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?

4. ## 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).

5. ## Re: Permutations with different numbers of objects

I understand now.

So
n= (3^4)*(2^3)
= 648

If so, thanks!

6. ## Re: Permutations with different numbers of objects

Originally Posted by qwertyasd
I understand now.

So
n= (3^4)*(2^3)
= 648

If so, thanks!
That's correct.