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

For a set of $5$ true-or-false questions,no student has written all the correct answers,and no $2$ students have given the same sequence of answers. What is the maximum number of students in the class,for this to be possible?

How many numbers consisting of $5$ digits can be formed in which the digits $3, 4$ and $7$ are used only once and the digit $5$ is used twice?

There are $15$ buses running between Delhi and Mumbai. In how many ways can a man go to Mumbai and return by a different bus?

In a circus, there are $10$ cages to accommodate $10$ animals. Out of these, $4$ cages are so small that $5$ specific animals cannot enter them. In how many ways is it possible to accommodate the $10$ animals in these $10$ cages?

There are $12$ volleyball players in all in a college,out of which a team of $9$ players is to be formed. If the captain always remains the same,then in how many ways can the team be formed?

Vedclass Test Series

Exam Paper Generator

Online Exam Module