Question

A party of 5 persons sit at a round table .Find the odds
againts the two specified persons sitting next to each other.

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{ A party of 5 persons sit at a round table .Find the odds }\hspace{.33em}\\~\\
& \normalsize \text{ againts the two specified persons sitting next to each other.}\hspace{.33em}\\~\\
& a.)\ 3 \hspace{.33em}\\~\\
& b.)\ 1 \hspace{.33em}\\~\\
& c.)\ 4 \hspace{.33em}\\~\\
& d.)\ \normalsize \text{None of these} \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

n persons can sit around a table in (n-1)! factorial ways
5 people can sit in 4! ways
group 2 of them together
now 5 people can sit in 3! ways but these guys can switch positions so multiply by 2!
hence the odds of these happening is 1/2 i guess im not sure whether b is your answer but thats my answer hope that helped

Answer 3

answer given is b.)

Answer 4

u said odds=1/2 but option b.)=1 ?

Answer 5

there are no specified persons, and odds tend to be given as a ratio

Answer 6

format for odds: for:against

so i spose the options are the 'against' side of it

Answer 7

there are 12 ways and 3 of them include 2 persons sitting together

3:9=1:3 -> for

3:1-> against

so i think it is option a.) but answer in book is option b.)

Answer 8

Pr= chances for/ total chances
odds = chances for: chances against

in this problem, Pr= 1/2
the 2 in the bottom is chances for + chances against
1+chances against=2
chances against= 1

thus the odds are 1:1

Answer 9

u mean out of 12 , 6 share two persons sitting next to each other

Answer 10

or out of 12, 6 don't have the two next to each other.
I am assuming hahd did it correctly (but it seems ok)

Answer 11

seat the 1st person (called O)

then there are 4 positions left (X,X,Z,Z)

2 of the positions the 2nd person cant sit (X and X) and 2 position they can (Z and Z)

that is a ratio of 2 to 2 or 1 to 1