Home
Class 12
MATHS
There are 5 different colour balls and 5...

There are `5` different colour balls and `5` boxes of colours same as those of the balls. The number of ways in which one can place the balls into the boxes, one each in a box, so that no ball goes to a box of its own colour is

A

`40`

B

`44`

C

`45`

D

`60`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `(D_(n))/(n!)-(D_(n-1))/((n-1)!)=((-1)^(n))/(n!)` gives
`(D_(n))/(n!)=sum_(r=2)^(n)((D_(r ))/(r!)-(D_(r-1))/((r-1)!))=sum_(r=2)^(n)((-1)^(r ))/(r!)`
`impliesD_(n)=n!sum_(r=2)^(n)((-1)^(r ))/(r!)`
`:. D_(5)=5!((1)/(2!)-(1)/(3!)+(1)/(4!)-(1)/(5!))=44`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|2 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Matching Column Type|1 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE PUBLICATION|Exercise Sovled Examples|22 Videos

Similar Questions

Explore conceptually related problems

There are 4 balls of different colours and four boxes of colours same as these of the balls the number of ways in which the balls one in each box would be placed such that a ball does not go to a box of its own colour is

There are four balls of different colours and four boxes of colours same as those of the balls. Find the number of way in which the balls ,one in each box,of its own colour.

The number of ways in which 5 letters can be posted in 10 letter boxes is

There are greetings cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly 4 of the cards go into envelopes of respective colour is,

The number of ways in which 6 different balls can be put in two boxes of different sizes so that no box remain empty is :

Fifteen identical balls have to be put in five different boxes. Each box can contain any number of balls. The total number of ways of putting the balls into the boxes so that each box contains at least two balls is equal to a. .^9C_5 b. .^10 C_5 c. .^6C_5 d. .^10 C_6

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.

The total number of ways in which 5 balls of different colours can be distributed among 3 persons, so that each person gets atleast one ball is

There are 2 identical white balls, 3 identical red balls, and 4 green balls of different shades. Find the number of ways in which they can be arranged in a row so that atleast one ball is separated from the balls of the same color.

Five balls of different color are to be placed in three boxes of different size. Each box can hold all five. In how many different ways can we place the balls so that no box remains empty?