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)
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
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