I could have done better. But it is still good, given the fact that I am not an American.
I am Indonesian
here it is
Imagine the letters are in a hat, and you need to choose them in the right order. At first there are 12 letters in the hat, and you need to pull a P, your chances are 1 in 12. If you get that, then you need to pull the E out of the remaining letters, chances of doing so are 1/11. Next you need to pull an N, but there are 3 in the remaining letters, so 3/10... and so forth. Formula is below.
1/(1/12 * 1/11 * 3/10 * 2/9 * 1/8 * 1/7 * 1/6 * 1/5 * 2/4 * 1/3 * 1/2 * 1/1)
- There are 12! ways to randomly order Pennsylvania if all letters are distinguishable.
- There is only 1 way that works if all letters are distinguishable.
- Because there are 3 Ns and 2 As, there are 3! = 6 ways the Ns can be ordered and 2! = 2 ways the As can be ordered.
- Therefore, there are 6 * 2 = 12 ways when using distinguishable letters for every 1 way when common letters are indistinguishable.
- Our answer is 12 / 12! = 1 / 11! = 1 / 39916800. (This is the same answer plattitude got.)
Also, when 4 letters are scrambled there is a 1/24 chance of it being the same, but in Ohio's case it is doubled because of the two "O"'s in it's name. This means the odds are 1/12.
Multiplying the 2 fractions: 1/12*2/5=2/60. And we can simplify that by dividing each side by 2.
There is a 1/30 chance for "Ohio" to be scrambled as "Ohio" on this quiz.
Missed deleware and louisiana
For most of these I just saw a letter that identified the state. Y for Wyoming, all the Cs in Connecticut, or the L in Louisiana.
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