Multinomial Theorem

Q.

One or more options can be correct:
Find the coefficient of $x^{10}$ in $(1-x^7)(1-x^8)(1-x^9)(1-x{)}^{-3}$

1. 

2. 

3. 

4. 

Q.

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

1. 192

2. 70

3. 64

4. 35

Q.

In how many ways 3 friends Ram, Rajat and Rupesh having 6 one rupee coins, 7 one rupee coins, 8 one rupee coins respectively donate 10 rupee coin collectively?

1. 45

2. 47

3. 50

4. 40

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. 

3. 

4. 

Q.

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

1. 35

2. 70

3. 64

4. 192

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. 

3. 

4. 

Q.

In how many ways 3 friends Ram, Rajat and Rupesh having 6 one rupee coins, 7 one rupee coins, 8 one rupee coins respectively donate 10 rupee coin collectively?

1. 50

2. 47

3. 40

4. 45

Q.

One or more options can be correct:
Find the coefficient of $x^{10}$ in $(1-x^7)(1-x^8)(1-x^9)(1-x{)}^{-3}$

1. 

2. 

3. 

4. 

Q. Number of ways to divide $21$ different things into two groups of $10$ and $11$ things are?

1. $\frac{21!}{8!\times 10!}$
2. $\frac{21!\times 10!}{11!}$
3. $\frac{21!}{8!\times 11!}$
4. $\frac{21!}{10!\times 11!}$

Q. $15$ identical jewels are to be distributed between $P,Q,R$ and $S$. Find the number of ways in which $P$ gets a maximum of $5$ and $Q$ gets at least $2$ jewels.

1. $560$
2. $120$
3. $440$
4. $680$