There are four balls of different colours and | vedclass

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

Question

(C) This is a classic problem of derangements,where $n$ items are placed in $n$ containers such that no item is in its correct container.The number of

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(C) This is a classic problem of derangements,where $n$ items are placed in $n$ containers such that no item is in its correct container.The number of derangements of $n$ objects,denoted by $D_n$,is given by the formula:$D_n = n! \left( 1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \dots + (-1)^n \frac{1}{n!} \right)$For $n = 4$:$D_4 = 4! \left( \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} \right)$$D_4 = 24 \left( \frac{1}{2} - \frac{1}{6} + \frac{1}{24} \right)$$D_4 = 24 \left( \frac{12 - 4 + 1}{24} \right)$$D_4 = 12 - 4 + 1 = 9$Thus,there are $9$ ways to place the balls such that no ball goes into the box of its own colour.

There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls,one in each box,could be placed such that a ball does not go to the box of its own colour is

Similar Questions

How many numbers lying between $99$ and $1000$ can be formed using the digits $2, 3, 7, 0, 8, 6$,if each digit can be used only once in each number?

$A$ man has $10$ friends. In how many ways can he invite one or more of them to a party?

$A$ car can hold $2$ people in the front seat and $1$ person in the rear seat. If among $6$ persons $2$ can drive,then the number of ways in which the car can be filled is

$^nC_r + ^{n-1}C_r + ...... + ^rC_r$ =

In how many ways can a committee consisting of one or more members be formed out of $12$ members of the Municipal Corporation?

Vedclass Test Series

Exam Paper Generator

Online Exam Module