When asked about Melania Trump's Republican National Convention speech Monday night, and whether or not two key passages were plagiarized from Michelle Obama Michelle LeVaughn Robinson ObamaTo honor Justice Ginsburg's legacy, Biden should consider Michelle Obama National Urban League, BET launch National Black Voter Day The Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill MORE's 2008 Democratic convention speech, Trump campaign chairman Paul Manafort dismissed the possibility, saying, among other reasons, "These were common words and values."

I thought: "Well, yes — but what about the ordering of those 'common words'?"

I'm an astrophysicist — an associate professor of physics at McGill University. Calculating probabilities is how I — and all observational physicists — earn bread and butter.

So let's accept Manafort's statement as true.

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Let's ignore that having the same thematic thrust between Trump's passage and Obama's passage feels a little coincidental. Who isn't for hard work? I agree with Manafort; it's a common value.

Let's forget the fact that there are lots of synonyms that Melania Trump could have used instead of "word is your bond," "achievements" and "treat people with ... respect," which would have made her passage deviate from the first lady's passage.

And let's just ask the simple, calculable question: What is the probability that, giving Melania Trump the same distinct phrases as used by Michelle Obama, she uses them in precisely the same order?

After examining the passages from the two speeches, here are the phrases which I regard as "distinct" (i.e., not necessarily joinable with a nearby phrase) that I see in both Trump's passage and Obama's passage: "values," "work hard for what you want in life," "word is your bond," "do what you say," "treat people with ... respect," "pass [them] on to many generations," "because we want our children," "in this nation," "to know," "the only limit," "your achievements," "your dreams," "willingness to work for them."

That totals 14 distinct phrases. They could be used in almost any ordering, with additional wording, to express the same themes as Trump and Obama did. So Trump could have taken those 14 phrases, put them in any order, and still write a similarly themed speech as Obama. But Trump used the same ordering as Obama did. The probability of that happening depends on the total number of unique orderings — the number of permutations — those 14 phrases have.

That's an easy calculation. To see that calculation, let's create a single unique ordering of the 14 distinct phrases. First, choose one of the 14 phrases, and write it down. There are 14 possibilities to start the ordering off. Then, choose one of the 13 remaining phrases, and list it under the first. There are 13 completely independent possible orderings. Already, we have 14*13=182 possible permutations — and that's just the first two phrases.

For the third phrase, we choose from the 12 remaining phrases; then one of the remaining 11 phrases, and on and on, all the way down until there's only one phrase left, and you add that at the end.

Doing so, you can see, the total number of possible orderings of those 14 phrases that Trump has in common with Obama is 14*13*12*11*10*9*8*7*6*5*4*3*2*1.

You might remember doing this calculation in high school calculus: The number of permutations of N distinct objects is written as N! ("N factorial") where the exclamation mark is a mathematical operator, and not an indicator of how excited we are at doing a mathematical calculation on the likelihood a possible future first lady committed plagiarism against her predecessor.

According to this calculation, there are a grand total of about 87 billion different permutations for those 14 distinct phrases. That's 87,000,000,000 — about the number of stars there are in the Milky Way.

Now, a typical criticism might be, "Hold up, I think that there are phrases which you've taken as distinct, but they can only be used together and in one order, and so there are fewer phrases than you say." Okay, let's look at that. Take the 14 phrases above. Put them out onto a table. Mix them up. Show them to three people (independently) and ask them. "Which of these phrases must be paired, and in what order? Choose no more than three pairs [to keep the sample size small]."

If all three people pick a pair of phrases that I call distinct, and put them in the same order as both Trump and Obama did, then you may call those which I call "two phrases" as "one phrase", and that would reduce the total number of distinct phrases from 14 to 13 (or, fewer, if they find more).

But I hold that no three people will see such an association, and that the 14 phrases I wrote above are distinct phrases, and so randomizable as such.

Just to note: If there were only 13 distinct phrases, instead of 14, the chances drop from 1 in 87 billion to 1 in 6.2 billion, and in no way alters the conclusion, and remains astronomically unlikely.

So never mind Manafort's claim that there are a limited number of words in the English language. For Melania Trump to have gotten all 14 of those phrases in the same order as Michelle Obama did at the 2008 Democratic National Convention is a chance of 1 in 87 billion — about 7,000 times less likely than winning Ontario's Lotto 6/49.

Highly unlikely.

Sad!

Rutledge is an associate professor in the Department of Physics at McGill University in Montreal, Québec, Canada. This essay is based on a Facebook post by the author on July 19, 2016, which may be found here.

The views expressed by contributors are their own and not the views of The Hill.