Dearrangement

Q.

The total number of ways in which a begger can be given at least one rupee from four $25$-paise coins, three $50$ paise coins and $2$ one-rupee coins, is

1. $54$

2. $50$

3. $52$

4. None of these

Q. There are five students $S_1,S_2,S_3,S_4$ and $S_5$ in a music class and for them, there are five seats $R_1,R_2,R_3,R_4$ and $R_5$ arranged in a row, where initially the seat $R_i$ is allotted to the student $S_i,$ $i=1,2,3,4,5$. But, on the examination day, the five students are randomly allotted the five seats.

The probability that, on the examination day, the student $S_1$ gets the previously allotted seat $R_1$, and $NONE$ of the remaining students gets the seat previously allotted to him/her is

1. $\frac{3}{40}$
2. $\frac{1}{8}$
3. $\frac{7}{40}$
4. $\frac{1}{5}$

Q. A man has $7$ letters for his $7$ friends. The letter are kept in the envelopes at random. The number of ways in which exactly $3$ letters are going to correct envelope and rest $4$ letters are going to the wrong envelopes is

1. $210$
2. $315$
3. $350$
4. $420$

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. 264
2. 265
3. 53
4. 67

Q. There are $5$ people and $5$ different pairs of shoes. If each person chooses at random one right shoe and one left shoe, then the number of combinations that can be made in which no one gets a correct pair is

1. $44$
2. $120$
3. $2880$
4. $5280$

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.

The number of ways in which all the letters of the word $GARDEN$ can be arranged such that no letter is in its original position is

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. $44$
2. $53$
3. $67$
4. $265$

Q. $3$ letters are to be placed in $3$ addressed envelopes. If the letters are placed randomly, then the probablity that all letters are in right envelopes, is

1. $\frac{1}{4}$
2. $\frac{1}{8}$
3. $\frac{1}{3}$
4. $\frac{1}{6}$

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. 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. A man has $7$ letters for his $7$ friends. The letter are kept in the envelopes at random. The number of ways in which exactly $3$ letters are going to correct envelope and rest $4$ letters are going to the wrong envelopes is

1. $210$
2. $315$
3. $350$
4. $420$

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. 264
2. 265
3. 53
4. 67