SOLUTION: How many ways can you rearrange 12 eggs ? Do you use 12! Or permutations ?

Question 601074: How many ways can you rearrange 12 eggs ? Do you use 12! Or permutations ?
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

1 way. Presumably one egg is just like the other, at least for most practical purposes. Hence, the number of arrangements of a dozen eggs must be the same as the number of arrangements of the letters AAAAAAAAAAAA, namely 1. If they are different, as in a dozen differently decorated easter eggs, then yes, 12! arrangements.

John

My calculator said it, I believe it, that settles it

Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
There are 12 places to pick a place for the 1st egg,
For each of those 12 places, there remain 11 places to put the 2nd egg.
That 12ｷ11 ways to place the first two 3ggs.

Factoriala ARE permutations. The best way is to think it out: There are 12 ways to place egg #1 in the carton. For each of those 12 ways to place the 1st egg, there remain 11 places in the carton to place egg #2. That's 12ｷ11 ways to place the first 2 eggs in the carton. For each of those 12ｷ11 ways to place the 1st 2 eggs, there remain 10 places in the carton to place egg #3. That's 12ｷ11ｷ10 ways to place the first 3 eggs in the carton. For each of those 12ｷ11ｷ10 ways to place the 1st 3 eggs, there remain 9 places in the carton to place egg #4. That's 12ｷ11ｷ10ｷ9 ways to place the first 4 eggs in the carton. For each of those 12ｷ11ｷ10ｷ9 ways to place the 1st 4 eggs, there remain 8 places in the carton to place egg #5. That's 12ｷ11ｷ10ｷ9ｷ8 ways to place the first 5 eggs in the carton. For each of those 12ｷ11ｷ10ｷ9ｷ8 ways to place the 1st 5 eggs, there remain 7 places in the carton to place egg #6. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7 ways to place the first 6 eggs in the carton. For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7 ways to place the 1st 6 eggs, there remain 6 places in the carton to place egg #7. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6 ways to place the first 7 eggs in the carton. For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6 ways to place the 1st 7 eggs, there remain 5 places in the carton to place egg #8. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5 ways to place the first 8 eggs in the carton. For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5 ways to place the 1st 8 eggs, there remain 4 places in the carton to place egg #9. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4 ways to place the first 9 eggs in the carton. For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4 ways to place the 1st 9 eggs, there remain 3 places in the carton to place egg #10. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3 ways to place the first 10 eggs in the carton. For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3 ways to place the 1st 10 eggs, there remain 2 places in the carton to place egg #11. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2 ways to place the first 11 eggs in the carton. For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2 ways to place the 1st 11 eggs, there remain only 1 place in the carton to place egg #12. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2ｷ1 ways to place all 12 eggs in the carton. Answer: 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2ｷ1 = 12! That's also the number of permutations of 12 things taken all 12 at a time. nPn or P(n,n) = n! Edwin

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