Dearrangement

Q. Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2, the number of ways it can be done is -

1. 53
2. 264
3. 265
4. 67

Q.

Six$‘+‘$and four $‘-‘$signs are to be placed in a straight line so that no two $‘-‘$ signs come together, then the total number of ways are?

1. $15$

2. $18$

3. $35$

4. $42$

Q. A problem in statistics is given to $3$ students $A,B,C$. This chances of solving problems are $1/3,1/4$ and $1/5$ respectively. If all of $3$ try independently what is probability that exactly two students solve the problem.

Q. Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is

1. 53
2. 67
3. 264
4. 265

Q.

There are four balls of different colors and four boxes of colors same a 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 a box of its own color is?

1. $8$

2. $7$

3. $9$

4. None of these

Q. Three letters are dictated to three persons and an envelope is addressed to each of them the letters are inserted into the envelopes at random, so that each envelope contains exactly one letter. Find the probability that at least one letter is in proper envelope.

Q.

5 countries president and prime minister went for summit. If all 5 prime minister shake hand to president at random, in how many ways they can shake hand if none of the same country PM shake hand to that country president.

1. 9

2. 120

3. 44

4. 24

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

Q. The total number number of ways in which all the digits of the number $79853$ can be arranged such that no digit will occur in its original position as given in the number is

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

Q.

If 5 letters are taken out of 5 different envelopes. In how many ways, can they be reinserted in the envelopes so that no letter goes to its original envelopes?

1. 9

2. 44

3. 120

4. 24

Q.

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 box of its own colour is

1. 9

2. 8

3. 7

4. 6

Q. The number of ways in which $5$ balls numbered $1-5$ can be placed in $5$ boxes numbered as $1-5$ (each box can accomodate one ball only) when

1. all the balls should be kept on correspnding numbered boxes is $5$
2. one ball is not kept in correspnding numbered box is $1$
3. three balls are not kept in correspnding numbered boxes is $20$
4. four balls are not kept in correspnding numbered boxes is $45$

Q. Number of $4$ digit numbers of the form
$N=abcd,$ which satisfy following conditions :
$\left(i\right)4000\le N<6000$
$\left(ii\right)N$ is a multiple of $5$
$\left(iii\right)3\le b<c\le 6$ is equal to

1. $16$
2. $12$
3. $4$
4. $24$

Q.

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 box of its own colour is

1. 8

2. 7

3. 9

4. 6