Division and Distribution into Groups of Unequal Sizes

Q.

The number of ways in which $5$ identical balls can be kept in $10$ identical boxes. If not more than one can go into a box is?

1. ${}^{10}P_5$

2. ${}^{10}C_5$

3. $5$

4. $1$

Q. The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball, is ?___

1. 75
2. 150
3. 210
4. 243

Q. No. Of ways in which 12 identical balls can be put in 5 different boxes in a row, if no box remains empty is

1. 
2. 
3. 
4. 

Q.

The number of ways in which 5 identical balls can be kept in 10 identical boxes, if not more than one can go into a box, is

1. 

2. 

3. 1

4. 5

Q. A committee of 5 is to be formed from 6 boys and 5 girls, . The number of ways that the committee can be formed so that the committee contains at least one boy and one girl is

1. 445
2. 440
3. 455
4. 450

Q. The position vector of a point P is $\overrightarrow{r}=x\overrightarrow{i}+y\overrightarrow{j}+z\overrightarrow{k}$ where x and y are positive integers and $\overrightarrow{a}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ If $\overrightarrow{r}.\overrightarrow{a}=10$, then the number of possible positions of P is :

1. 48
2. 36
3. 72
4. 24