Question:
There are $5$ letters and $5$ different envelopes. The number of ways in which all the letters can be put in wrong envelope, is
There are $5$ letters and $5$ different envelopes. The number of ways in which all the letters can be put in wrong envelope, is
Updated On: Apr 19, 2024
- 119
- 44
- 59
- 40
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Required numbers
$=5 !\left[1-\frac{1}{1 !}+\frac{1}{2 !}-\frac{1}{3 !}+\frac{1}{4 !}=\frac{1}{5 !}\right]=44$
if $r(0 \leq r \leq n)$ objects occupy the original places and none of the remaining $(n-r)$ objects occupies its original places then the number of such arrangements $={ }^{n} C_{r}(n-r) !$
$\left[1 \frac{1}{1 !}+\frac{1}{2 !}-\frac{1}{3 !}+\ldots+(-1)^{n-2} \frac{1}{(n-r) !}\right]$
$=5 !\left[1-\frac{1}{1 !}+\frac{1}{2 !}-\frac{1}{3 !}+\frac{1}{4 !}=\frac{1}{5 !}\right]=44$
if $r(0 \leq r \leq n)$ objects occupy the original places and none of the remaining $(n-r)$ objects occupies its original places then the number of such arrangements $={ }^{n} C_{r}(n-r) !$
$\left[1 \frac{1}{1 !}+\frac{1}{2 !}-\frac{1}{3 !}+\ldots+(-1)^{n-2} \frac{1}{(n-r) !}\right]$
Was this answer helpful?
0
0
Top Questions on permutations and combinations
- In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A, B and C . A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is _______ .
- JEE Main - 2024
- Mathematics
- permutations and combinations
- A local restaurant has 16 vegetarian items and 9 non-vegetarian items in their menu. Some items contain gluten, while the rest are gluten-free.
One evening, Rohit and his friends went to the restaurant. They planned to choose two different vegetarian items and three different non-vegetarian items from the entire menu. Later, Bela and her friends also went to the same restaurant: they planned to choose two different vegetarian items and one non-vegetarian item only from the gluten-free options. The number of item combinations that Rohit and his friends could choose from, given their plan, was 12 times the number of item combinations that Bela and her friends could choose from, given their plan.
How many menu items contain gluten?- XAT - 2024
- Quantitative Ability and Data Interpretation
- permutations and combinations
- The lines $L_1, L_2, \ldots, L_{20}$ are distinct. For $n = 1, 2, 3, \ldots, 10$, all the lines $L_{2n-1}$ are parallel to each other, and all the lines $L_{2n}$ pass through a given point $P$. The maximum number of points of intersection of pairs of lines from the set $\{L_1, L_2, \ldots, L_{20}\}$ is equal to:
- JEE Main - 2024
- Mathematics
- permutations and combinations
- If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at 315th position in this arrangement is
- JEE Main - 2024
- Mathematics
- permutations and combinations
- Let the set $S = \{2, 4, 8, 16, ..., 512\}$ be partitioned into 3 sets $A, B, C$ with equal number of elements such that $A \cup B \cup C = S$ and $A \cap B = B \cap C = A \cap C = \phi$. The maximum number of such possible partitions of $S$ is equal to:
- JEE Main - 2024
- Mathematics
- permutations and combinations
View More Questions
Questions Asked in VITEEE exam
- Two identical blocks A and B, each of mass 'm' resting on a smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block 'C' (mass m) moving with a speed v along the line joining A and B collides with A. the maximum compression in the spring is
- VITEEE - 2023
- work, energy and power
- Assertion :
The binding energy of the nucleus increases with the increase in atomic number.
Reason :
Heavier elements have a greater number of non-radioactive isotopes than radioactive isotopes. - The half-life of radioactive radon is 3.8 days. The time at the end of which \(\frac{1}{20}th\) of the Radon sample will remain undecayed is (given log10e=0.4343)
- Which element has more electron gain enthalpy among chalcogen group?
- VITEEE - 2022
- sulphur
- Coin is tossed till heads is obtained what is expectation of no. of coin tosses
- VITEEE - 2022
- Random Variables
View More Questions
Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.