Miles has 4 Lego people in his Lego town. A Lego person consists of exactly 1 set of legs, a torso, and a head. All of these body parts are distinct. Miles' son comes in and takes apart the Lego people. How many different sets of 4 Lego people can be created from the pieces?

Answer 1

Assembling the head, there are 4! ways.
Same for each of the three other parts.
Total number of ways = 4!4!4!4!
But we can arrange the 4 people in 4! different orders, so total number of sets of 4 people
= (4!)^4/(4!)
=(4!)³

Answer 2

I don't remember the formulas or anything, but just thinking about it:

for the first guy you have 4 heads X 4 torsos X 4 legs
2nd guy has 3 heads X 3 torsos X 3 legs
then 3rd has 2X2X2
last guy has 1X1X1

so 4X4X4X3X3X3X2X2X2X1X1X1
in other words
4X3X2X1X4X3X2X1X4X3X2X1
or
(3)*4!

Answer 3

oops sorry not 3*4!, 4!*4!*4!. parent is right, i'm wrong

Answer 4

@allthehomework needs to stop answering questions since he/she often has to apologize or is not 100% sure of what he/she has written.

=(