20 persons are invited for a party. In how ma | vedclass

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

Question

(B) Total number of persons $= 20 + 1 = 21$.Let the host be $H$ and the two particular persons be $P_1$ and $P_2$.Since $P_1$ and $P_2$ must sit on ei

Vedclass · Accepted Answer

$2 	imes 18!$

Vedclass · Answer

(B) Total number of persons $= 20 + 1 = 21$.Let the host be $H$ and the two particular persons be $P_1$ and $P_2$.Since $P_1$ and $P_2$ must sit on either side of the host,we treat the group $(P_1, H, P_2)$ as a single unit.This leaves $21 - 3 = 18$ other persons plus the $1$ unit,making a total of $19$ entities to be arranged in a circle.The number of ways to arrange $n$ items in a circle is $(n-1)!$,so $19$ entities can be arranged in $(19-1)! = 18!$ ways.Within the unit $(P_1, H, P_2)$,the two persons $P_1$ and $P_2$ can be arranged in $2! = 2$ ways (i.e.,$P_1HP_2$ or $P_2HP_1$).Therefore,the total number of ways is $2 	imes 18!$.

$20$ persons are invited for a party. In how many different ways can they and the host be seated at a circular table,if two particular persons are to be seated on either side of the host?

Similar Questions

The number of ways of arranging $2$ red,$3$ white,and $5$ yellow roses of different sizes into a garland such that no two yellow roses come together is

In how many ways can $15$ members of a council sit along a circular table,when the Secretary is to sit on one side of the Chairman and the Deputy Secretary on the other side?

The number of ways in which $6$ boys and $5$ girls can sit at a round table,if no two girls are to sit together,is

If $20$ beads of two different colors are to be arranged in a necklace such that they alternate,and there are $10$ beads of each color,then what is the number of ways to arrange them?

$A$ couple can sit with $6$ guests around a circular table. In how many ways can they sit if the couple sits in consecutive seats?

Vedclass Test Series

Exam Paper Generator

Online Exam Module