Question 1023138: cAn algebra class has 12 students and 12 desks. For the sake of variety, students change the seating arrangement each day.
How many days must pass before the class must repeat a seating arrangement?
days must pass before a seating arrangement is repeated. ANSWERE: 479001600
Suppose the desks are arranged in rows of 4. How many seating arrangements are there that put Larry, Moe, Curly, and Shemp in the front seats?
What is the probability that Larry, Moe, Curly and Shemp are sitting in the front seats?
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Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i think what may be happening is this.
there would be 3 rows of 4.
the first row has to be composed of larry, moe, curly and shemp.
that's 4 people who can be arranged in 4! ways.
4! is the same as p(4,4).
4! = 4*3*2*1 = 24.
p(4,4) = 4! / (4-4)! = 4! / 0! = 4! / 1 = 4! = 4*3*2*1.
so 4! is the same as a permutation of 4 things taken 4 at a time.
once you've got the first row taken care of, the rest of the rows can be arranged in any way, which means that they can be arranged in 8! ways.
8! = 40320.
if correct, then the total number of ways when larry, moe, curly, and shemp are in the first row would be 24 * 40320 = 967680.
i looked at it another way.
24 ways for the first row.
the second row can take any 4 from the remaining 8, and order is important.
that would be p(8,4) = 1680 ways.
the third row can take any 4 from the remaining 4, and order is important.
that would be p(4,4) = 24 ways.
the total ways, using this second method, should be 24 * 1680 * 24 = 967680.
same answer, which indicates both methods are comparable.
if correct, your answer should be 967680.
i think this is correct.
these problems are very difficult to confirm because of the many possible combinations.
my method is to reduce the problem as simple as possible and then see if i can created the situation and detail all the possible solutions.
i did that with 6 people and then taking them 2 at a time.
it looks like the methods i showed you are correct using this simpler example, so i went with that.
hopefully it's what you need.
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