Ok, we were arguing about this at work yesterday:

There are 3 people. Each person has a green, blue, yellow, orange, and purple shirt. (5 shirts for each person).

What are the total number of combinations they can wear?

It seems really easy, but our answers range from 125 to 9,700,000.

 

It depends. Can they swap shirts? Can they wear multiple shirts? Do they have to wear a shirt at all? All these parameters add to (or reduce) the complexity of the problem.

 

If they can't swap, be naked, or wear multiple shirts, then I think the answer is 125

 

They can't swap, they only wear their own shirts. Skin isn't an option either. They can wear the same color on the same day.

 

Nolonger-----my answer was 125 as well.
5 options for each person
5x5x5=125

My buddy came up with over 9 million

 

Hmm, I would think you need to account for there being "3" people in the equations as well...... Math is definitely not my strong point, though.

 

The 3 is accounted for..... 5x5x5

If there were 4 people, it would be 5x5x5x5

 

125

 

The majority here think it's 125 and they are absolutely correct.

- Jack

 

125 Is the answer if they can have more than one person wearing the same color shirt. If not then the answer is 60.

 

Bonus question - how many combinations if they can wear more than one shirt at a time?

 

it's not easy because you did not define "combination".

if you meant "how many combinations of 3 people wearing one of 5 shirts, colored... etc.", then the answer is 125.

 

I think the answer is (5Factorial) cubed if they can wear as many as all 5 shirts at once. if they can only wear up to 4 at a time, then the answer's 4!**3. I'm assuming i'm remembering correctly, but i think that's right.
you didn't specify how many more than one they could wear at once, and i'm assuming 5 as the upper limit.

try this: for 2 as the upper limit:
each guy can wear 20 combinations of 2 shirts at a time, chosen from a set of 5, so that would be 8000 combinations.

for 3 as the upper limit, each guy can wear 60 combinations, for a total of 60*60*60= 21600.

i think this is right.

 

OK.. Joe - 1) each can wear between 1-5 shirts.

To further compound it, how many different total unique combinations would there be if all 3 people could all wear 1-5 shirts and you considered each order of shirts as a single unique item.

 

math minor here. 125.