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?
bud you already asked this question and got an answer.
jiskha dot com/display.cgi?id=1369923935
ur answer was wrong
You were quite right, Andrew.
The answer should have been
(4!)^4/(4!)²
4! is the number of ways to assemble a single body part.
Since there are 4 body parts to assemble, we have (4!)^4 ways to assemble the 4 people where order counts.
Since there are 4! permutations of the people, as well as 4! permutations of the body parts, we divide by (4!)² when order does not count.
So the final answer is
(4!)^4/(4!)²=24²=576
To determine how many different sets of 4 Lego people can be created from the pieces, we need to calculate the number of possible combinations.
First, let's consider the number of options for each body part. Since each body part is distinct, there are:
- Legs: 4 options
- Torso: 4 options
- Head: 4 options
To calculate the total number of combinations, we multiply the number of options for each body part:
4 options for Legs * 4 options for Torso * 4 options for Head = 64 combinations
Therefore, there are 64 different sets of 4 Lego people that can be created from the pieces.