Math error in Young Sheldon

In the season 3 episode 4 of Young Sheldon, titled Hobbitses, Physicses and a Ball With Zip, Sheldon asks himself the number of possible combinations on a bingo card. A question I'm sure I've asked myself at about his age (this is not a joke). Here are some pictures of the scene. Click on any image for a larger version.












The answer is absolutely wrong.

For the B,I,G, and O columns, the call-out boxes suggest the number combinations is 15!/(15!-5)!, but the actual number shown, 360,360 is equal to 15!/10!, which does equal 15*14*13*12*11, as shown. However, they forget to divide by 5!=120. In other words, the actual number of combinations for one of those columns is 15!/((15-10)! * 5!).

The same problem happens with the N column call-out (do I hyphenate that?) box?

As to the last image, I have no idea what that is trying to say.

The correct answer is [15!/((15-5)!*5!)]⁴ * [15!/((15-4)! * 4!)) ] = 111,007,923,832,370,565.

In conclusion, I formally accuse the writers of Young Sheldon for getting the math in the bingo scene wrong. The ironic thing is later in the Episode, Sheldon become obsesses with errors in the chronology of the Lord of the Rings. Hmmm.

There was also a similar scene involving the physics of a bowling ball. I'll bring up that separately.

That's unfortunate. In general most of the "Big Bang Theory" math was right, wasn't it?

Most professionals find Hollywood irksome due to perceived errors.

Gamblers almost always (the movie "21" ring a bell).

police officers almost always cringe sickeningly when a Hollywood cop takes a smidgen of powder and tests it for Cocaine by licking it or wiping it on the inside of their mouth. As one officer interviewed said, "no cop would EVER do that. You dont know what the substance is. It could be rat poison."

Drugs are always tested using chemical solutions packets they carry around.

Hollywood shows have a multitude of people working on any given show and the correct math may have been supplied and then lost in translation from paper to screen. Their job is to entertain not educate in this scenario

In the show's defense, Sheldon would have been right if he cared about the position of each number. The show asks "How many unique BINGO cards exist?" However, the formulas shown on the screen were still wrong, although the numerical answers would have been right.

If someone had asked me this question, or I asked myself, I would have used combinations, not permutations.

Interesting. I have seen home games where each column is in ascending order. That does not seem to be the standard, and cards shown in the screen shots are not ordered. They obviously had some help. It would be interested to know how the error occured. Maybe a more egregious error is found on the Bingo Wikipedia page which as of the posting disagrees with your calculation by a factor of half a trillion times or so.

Remember that, on a BINGO card, unless you are playing a game where you have to fill in all 24 numbers, the order of the numbers matters. Two cards that are identical except that one has 1 in the top left and 15 in the bottom right but the other has 15 in the top left and 1 in the bottom right are different, as the top rows, bottom rows, and both diagonals, have different winning combinations.

The main error I see is, in the first and second calculations, the denominators say (15! - 5)! and (15! - 4)! instead of (15 - 5)! and (15 - 4)!.
Also, you would think that Sheldon would know what "permutations" are, and use the corresponding symbol, rather than the combinations symbol multiplied by a factorial (i.e. something like P_15,5, or ₁₅P₅, rather than 5! multiplied by the symbol for (15)C(5)).

By my interpretation of "different", there are (15 x 14 x 13 x 12 x 11)⁴ x (15 x 14 x 13 x 12) unique cards.
You can make a case for diving the number by 2, since if you flip the card vertically, none of the winning combinations of numbers changes, but if you are playing a game that involves specific lines (e.g. "first to get a 2x2 square in the top two lines wins"), then you can't do that.

Quote: tringlomane

That's unfortunate. In general most of the "Big Bang Theory" math was right, wasn't it?

There is one episode of BBT where Sheldon mixes up ordinal and cardinal numbers (it's the one with the malfunctioning space toilet). Other than that everything they said seemed pretty good as far as I could tell.

Quote: TumblingBones

. Other than that everything they said seemed pretty good as far as I could tell.

Except the jokes.

Quote: Rigondeaux

Except the jokes.

I though some of them were great but maybe you have to have a math/sci background to think so. One of my favorites is were they are trying to figure out where to eat before going to see a movie. Sheldon puts so many constraints on the solution space that no solution exists. Wallowitz declares "there's only one solution" and they end up going without him. Sheldon's response ("He's right, it's the only solution") was the icing on the cake. I cracked up but probably because it reminded me of so many work-related situations.

Quote: Rigondeaux

Except the jokes.

That's a given.