If students are assigned to classrooms randomly, what are the odds the same 4 kids are together when they're assigned their 4th grade classroom?

(This actually happened!)

Quote:smoothgrhLet's say 4 kids are together in one 3rd grade classroom. The school has 4 classrooms with 22 kids for 88 kids total in each grade.

If students are assigned to classrooms randomly, what are the odds the same 4 kids are together when they're assigned their 4th grade classroom?

(This actually happened!)

Are we talking about a specific set of 4 kids or any 4 kids? Nevermind, that's a stupid question.

I would think the odds would be:

(3/21) * (2/20) * (1/19) = 0.00075187969 = 1-in-1330 odds.

Quote:smoothgrhLet's say 4 kids are together in one 3rd grade classroom. The school has 4 classrooms with 22 kids for 88 kids total in each grade.

If students are assigned to classrooms randomly, what are the odds the same 4 kids are together when they're assigned their 4th grade classroom?

(This actually happened!)

(21/87) * (20/86) * (19/85) = 266/21199

Quote:RSAre we talking about a specific set of 4 kids or any 4 kids? Nevermind, that's a stupid question.

It’s not a dumb question at all. Because it happens 100% of the time every year for some set of four kids. It’s impossible to sort 88 kids into 4 rooms without having at least 4 that end up together in consecutive years.

That’s the correct answer.Quote:ChesterDogI get approximately one in 79.7.

(21/87) * (20/86) * (19/85) = 266/21199

(But What makes you think the school is distributing kids randomly? If they know their job, they would try to keep friends together — and separate troublemakers.)

Quote:kubikulannThat’s the correct answer.Quote:ChesterDogI get approximately one in 79.7.

(21/87) * (20/86) * (19/85) = 266/21199

(But What makes you think the school is distributing kids randomly? If they know their job, they would try to keep friends together — and separate troublemakers.)

If you separate the troublemakers, you'll have them in every classroom. Concentrate them and you have three good classes and one potential zoo.

If I was doing the assigning,I'd divide them strictly on academics. First class would be the best students who will not be held back by students not up to their pace.

If those four students want to stay together, all they have to do is excel and be in the first group.

about 1 chance in 80Quote:smoothgrhIf students are assigned to classrooms randomly, what are the odds the same 4 kids are together when they're assigned their 4th grade classroom?

(This actually happened!)

probability is exactly: 266/21199

using pari/gp calculator

online here: https://pari.math.u-bordeaux.fr/gp.html

gp > a=4*(binomial(4,4)*binomial(84,18))/binomial(88,22);

gp > aDec=1.*a;

gp > a1chanceIn=1/aDec;

gp > a

%4 = 266/21199

gp > aDec

%5 = 0.012547761686872022265201188735317703665

gp > a1chanceIn

%6 = 79.695488721804511278195488721804511278

4 = there are 4 possible classrooms of equal size

binomial(4,4) = 4specificKidsChoose4

binomial(84,18) = 84otherKidsChoose18

binomial(88,22) = 88totalKidsChoose22

I used the hypergeometric probability solution as it is easily used for even more difficult type of questions like these. example: How about only 3 out of the 4 being in one classroom?

simulation shows this to be about correct

sum get lucky

Quote:kubikulann

(But What makes you think the school is distributing kids randomly? If they know their job, they would try to keep friends together — and separate troublemakers.)

Thanks everyone! My son and his 3 friends all live close to each other, so it was a happy coincidence they were in the same class last year. They're all together again, so I thought "what are the odds???"

However, you're probably right that it's not random, even though that's what the secretaries said—it's probably just the company line to say it's random. I'd agree with separating troublemakers!