There are 4 envelopes with addresses and 4 co | vedclass

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

Question

(C) The total number of ways to place $4$ letters into $4$ envelopes is $4! = 24$. This is a problem of derangements. The number of ways in which no l

Vedclass · Accepted Answer

$\frac{23}{24}$

Vedclass · Answer

(C) The total number of ways to place $4$ letters into $4$ envelopes is $4! = 24$. This is a problem of derangements. The number of ways in which no letter goes into its correct envelope is given by $D_4 = 4! \left( 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} \right) = 24 \left( \frac{1}{2} - \frac{1}{6} + \frac{1}{24} \right) = 12 - 4 + 1 = 9$. The probability is $\frac{9}{24} = \frac{3}{8}$. Wait,the standard interpretation of 'not going into the proper envelope' usually implies at least one is wrong,but the phrasing 'no letter goes into its correct envelope' refers to derangements. However,if the question implies the complement of 'all letters go into their correct envelopes',the probability is $1 - \frac{1}{4!} = 1 - \frac{1}{24} = \frac{23}{24}$.

There are $4$ envelopes with addresses and $4$ corresponding letters. The probability that no letter goes into its correct envelope is:

Similar Questions

There are $4$ distinct colored balls and $4$ boxes of the same colors as the balls. In how many ways can the balls be placed in the boxes such that no ball goes into a box of its own color?

Five letters are placed at random in five addressed envelopes. The probability that all the letters are not dispatched in the respective right envelopes is

$n$ distinct items $1, 2, 3, \dots, n$ are arranged in $n$ distinct positions $1, 2, 3, \dots, n$. What is the probability that at least three items are in their correct positions?

Three letters are placed at random into three envelopes addressed to three different people. The probability that all letters are placed in the correct envelopes is ..........

Let $A = \{x_1, x_2, x_3, x_4\}$ and $B = \{y_1, y_2, y_3, y_4\}$. $A$ function $f: A \to B$ is defined. The number of one-one functions such that $f(x_i) \neq y_i$ for $i = 1, 2, 3, 4$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module