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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?
3 answers
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
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
3 answers