n cadets have to stand in a row. If all possi | vedclass

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

Question

(A) The total number of ways to arrange $n$ cadets in a row is $n!$.To find the number of favorable cases where two particular cadets stand side by si

Vedclass · Accepted Answer

$\frac{2}{n}$

Vedclass · Answer

(A) The total number of ways to arrange $n$ cadets in a row is $n!$.To find the number of favorable cases where two particular cadets stand side by side,we treat them as a single unit.This leaves us with $(n - 1)$ units to arrange,which can be done in $(n - 1)!$ ways.The two particular cadets can be arranged among themselves in $2! = 2$ ways.Thus,the number of favorable cases is $2 	imes (n - 1)!$.The required probability is $\frac{2 	imes (n - 1)!}{n!} = \frac{2 	imes (n - 1)!}{n 	imes (n - 1)!} = \frac{2}{n}$.

$n$ cadets have to stand in a row. If all possible permutations are equally likely,then the probability that two particular cadets stand side by side is

Similar Questions

If $_{12}P_r = 1320$,then $r = ..........$

Ten chairs are numbered as $1$ to $10$. Three women and two men wish to occupy one chair each. First,the women choose the chairs marked $1$ to $6$,then the men choose the chairs from the remaining. The number of possible ways is

If the letters of the word $RACHIT$ are arranged in all possible ways and these words are listed in dictionary order,what is the rank of the word $RACHIT$?

Evaluate $\frac{n!}{(n-r)!}$ when $n=6$ and $r=2$.

By using the non-zero digits,the number of $5$ digit numbers that can be formed such that each number has the largest digit in its middle place and the digits in the number are distinct is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module