3 letters are placed randomly into 3 envelope | vedclass

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

Question

(A) Let the letters be $L_1, L_2, L_3$ and their corresponding envelopes be $E_1, E_2, E_3$.The total number of ways to place $3$ letters in $3$ envel

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(A) Let the letters be $L_1, L_2, L_3$ and their corresponding envelopes be $E_1, E_2, E_3$.The total number of ways to place $3$ letters in $3$ envelopes is $3! = 6$.The possible arrangements are: $(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), (3,2,1)$.We want exactly one letter in the correct envelope.If $L_1$ is in $E_1$,then $L_2$ and $L_3$ must be swapped ($L_2$ in $E_3$,$L_3$ in $E_2$). This is $1$ way.If $L_2$ is in $E_2$,then $L_1$ and $L_3$ must be swapped. This is $1$ way.If $L_3$ is in $E_3$,then $L_1$ and $L_2$ must be swapped. This is $1$ way.Total favorable ways $= 1 + 1 + 1 = 3$.The probability is $\frac{	ext{Favorable ways}}{	ext{Total ways}} = \frac{3}{6} = \frac{1}{2}$.

$3$ letters are placed randomly into $3$ envelopes. What is the probability that exactly one letter is placed in the correct envelope?

Similar Questions

$A$ bag contains $5$ blue and an unknown number $x$ of red balls. Two balls are drawn at random. If the probability of both of them being blue is $\frac{5}{14}$,then the value of $x$ is equal to

On her vacations,Veena visits four cities ($A, B, C$,and $D$) in a random order. What is the probability that she visits $A$ first and $B$ last?

Two bolts,two nuts,and three needles are in a box. Two parts are chosen at random from the box. What is the probability that one is a bolt and one is a needle?

In a certain lottery,$10,000$ tickets are sold and $10$ equal prizes are awarded. What is the probability of not getting a prize if you buy $10$ tickets?

$A$ box contains $8$ red and $x$ number of green balls. $3$ balls are drawn at random. If the probability that all $3$ balls are red is $\frac{7}{15}$,then the number of green balls $x$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module