Sixteen kids, 8 boys and 8 girls, are going on a train trip. Conveniently enough,
the train has precisely 8 benches and each bench seats precisely two kids. The
teacher assigns each kid at random to one of the eight benches. What is the
probability that none of the girls sits together with a boy on a bench?
- husoskiLv 79 months agoFavorite Answer
The exact order of students on the two benches doesn't matter. If there are both girls and boys on the same bench, at least 1 girl will sit next to at least 1 boy. The only way to get the desired result is is to have all the girls to seated on one bench and all the boys on the other.
There are C(16,8) ways to pick 8 kids for the first bench, and random assignments means that all of those are equally-likely. I'm using C(n,k) for the number of ways to choose k of n items, disregarding order. A calculator might have that as a key labeled "nCk" or "nCr". C(16,8) = 12,870.
Of the 12,870 ways to pick 8 kids for the first bench, only 2 of them (all boys or all girls) will have no girl seated next to a boy. So your probability is 2/12,870 = 1/6,435. That's about 0.000155.
- Anonymous9 months ago