If a party of n persons sit at a round table, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The total number of ways in which $n$ persons can sit at a round table is $(n - 1)!$. To find the number of ways where two specified individuals s

Vedclass · Accepted Answer

$(n - 3) : 2$

Vedclass · Answer

(B) The total number of ways in which $n$ persons can sit at a round table is $(n - 1)!$. To find the number of ways where two specified individuals sit together,we treat them as a single unit. This gives us $(n - 1)$ units,which can be arranged in $(n - 2)!$ ways. The two individuals can be arranged among themselves in $2!$ ways. So,the number of favourable ways is $2! 	imes (n - 2)!$. The probability $p$ that they sit together is $\frac{2! 	imes (n - 2)!}{(n - 1)!} = \frac{2}{n - 1}$. The odds against the event are given by $(1 - p) : p$. $(1 - \frac{2}{n - 1}) : \frac{2}{n - 1} = \frac{n - 3}{n - 1} : \frac{2}{n - 1} = (n - 3) : 2$.

If a party of $n$ persons sit at a round table,then the odds against two specified individuals sitting next to each other are

Similar Questions

If $3$ sisters and $8$ brothers are together playing a game,then the number of ways in which all the sisters and brothers are to be seated around a circle such that all the $3$ sisters are not seated together is

In how many ways can $4$ beads be selected and arranged in a necklace from $6$ distinct beads?

$21$ friends were invited for a party. Two round tables can accommodate $12$ and $9$ friends respectively. The number of ways of the seating arrangements of friends is:

Six persons $A, B, C, D, E$ and $F$ are to be seated at a circular table facing towards the centre. Find the number of ways this can be done if $A$ must have either $E$ or $F$ on his immediate right and $E$ must have either $F$ or $D$ on his immediate right.

In how many ways can $10$ people be seated around a circular table such that no two arrangements have the same neighbors? (Clockwise and counter-clockwise arrangements are considered the same.)

Vedclass Test Series

Exam Paper Generator

Online Exam Module