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?
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
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!
oops sorry not 3*4!, 4!*4!*4!. parent is right, i'm wrong
@allthehomework needs to stop answering questions since he/she often has to apologize or is not 100% sure of what he/she has written.
=(
To figure out the number of different sets of 4 Lego people that can be created from the pieces, we can break it down into each body part and count the possibilities:
1. Legs: Since a Lego person consists of exactly 1 set of legs, we have 4 options for the first person, 3 options for the second person, 2 options for the third person, and 1 option for the fourth person. Therefore, the number of leg combinations is 4 x 3 x 2 x 1 = 24.
2. Torso: Similarly, we have 4 options for the first person's torso, 3 options for the second person, 2 options for the third person, and 1 option for the fourth person. So, the number of torso combinations is also 24.
3. Head: The same pattern applies here. We have 4 options for the first person's head, 3 options for the second person, 2 options for the third person, and 1 option for the fourth person. Hence, the number of head combinations is 24.
To calculate the total number of different sets of 4 Lego people, we multiply the number of options for each body part: 24 x 24 x 24 = 13,824.
Therefore, there can be 13,824 different sets of 4 Lego people created from the pieces.