Multinomial Theorem

Q. A bag contains $30$ tokens numbered serially from $0$ to $29.$ The number of ways of selecting $3$ tokens from the bag, such that sum of numbers on them is $30$, is

1. $56$
2. $75$
3. $90$
4. $105$

Q.

Number of ways of selection of 8 letters from 24 letters of which 8 are a, 8 are b and the rest unlike, is given by

1. $2^7$

2. ${8.2}^8$

3. ${10.2}^7$

4. ${8.2}^7$

Q. Number of ways in which $25$ identical things can be distributed among five persons if each gets odd number of things is

1. ${}^{25}{C}_4$
2. ${}^{12}{C}_8$
3. ${}^{13}{C}_3$
4. ${}^{14}{C}_4$

Q. The number of non negative integral solution of $x_1+x_2+x_3+4x_4=20$ is

1. $536$
2. $443$
3. $655$
4. none of these

Q. If $4$ dice are rolled once, the number of ways of getting the sum as $10$ is

1. $64$
2. $80$
3. $84$
4. $126$

Q.

In how many ways can Rs. 16 be divided into 4 person when none of them get less than Rs. 3

1. 70

2. 35

3. 64

4. 192

Q. In how many ways the sum of upper faces of four distinct dice can be six?

1. $10$
2. $84$
3. $56$
4. None of these

Q. Number of ways in which $30$ identical things are distributed among six persons is:

1. ${}^{17}{C}_5$ if each person gets odd number of things.
2. ${}^{16}{C}_{11}$ if each person gets odd number of things.
3. ${}^{14}{C}_5$ if each person gets even number of things(excluding $0$).
4. ${}^{15}{C}_{10}$ if each persongets even number of things(excluding $0$).