Unfortunately, in a rather irritating case of genre-savviness, the bomb was, in fact, designed to go as soon as it was successfully disarmed, and now Rainbow's home is entirely flooded in strawberry jam. That hungers for pony flesh. As jam does.
While the cleaners are trying to hoover it all up, Rainbow plots her revenge. Unfortunately, most of the budget for the prank war went into the purchase of the Prism Poppers, and so you're pretty much on a shoestring. Fortunately, Rainbow does at least have one idea, considered by many to be the most heinous scheme ever conceived: spam her letterbox. As it happens, Wonderbolts such as herself receive a lot of fanmail, and she in turn has access to a lot of stamps, letters and other items to reply to any at any time back at the Wonderbolt Academy. She therefore decides to mail Black Bird a series of seemingly useless letters, filled with only seven digit numbers, direct to her mailbox, in different fonts from a typewriter, so she doesn't realise they are from the same pony, and hopefully either it will annoy her, receiving so much junk all at once, or result in her ignoring an important tax bill out of sheer frustration and get arrested for fraud, or something.
Gathering together all the supplies she got from the Academy for free, she decides to keep you occupied with a puzzle, to keep you from going stir crazy writing out idiotic letters. She's writing down different strings of seven numbers, basically to see if Black Bird tries to find meaning in these numbers that doesn't actually exist, but what Rainbow wants to know is: if she had some sort of machine that randomly assigns seven figure numbers to each of you, what are the chances both of you would wind up with an exact scramble of the other - that is to say, each number appears with the exact same frequency, but in a different order from the other? Basically, if 5 appears three times in Rainbow's number, it will appear three times in yours as well.
Real simple actually
the probability that 1 matching number is anywhere is 10/100 or 1/10, 2 matching is 10/100 times 9/90 or 90/900 witch is 1/10^2, so the chance all 7 digits match is 1/10^7 or 1 in million
unless you dont count the 1 in 10million they have the EXACTLY the same combo, witch in that case minus that from the previous answer
9399641
Not even close.
Each number can have their digits appear in different frequencies. For example, maybe all seven digits are different. Or maybe a number has three sets of two of the same digit plus one unique digit - there are 15 different possible configurations. Use that as a jumping off point.
* means multiply
This is actually fairly difficult since probability changes based on how many of the same number RD gets. The chance for your number to match her number on any one digit is 1/10. You take this to the power of the number of digits in one number, aka (1/10)7. Which is 1/(10 million).
We can use the formula [(N!/(G1!*G2!*...GX!) - 1)] {Where N is the number of digits, G is the number of the same numbers in the corresponding group, X is the number of groups, and the 1 is the number RD got (don't substitute).} to determine how many different shuffles of that number exist. Put that number over 107, and that's your probability. It goes anywhere from 0% (all seven numbers are the same) to 0.05% (all seven numbers are different).
This assumes that 122 has 3 different arrangements instead of 6. If it does have six, then it's 0.05%, because each number is considered a different number (D!/10D) {D is number of digits}
Answer possibly redacted by author.
9415983
Not redacted. Just no-one's solved it and I don't upload answers until someone gets it.