# Multinomial Theorem

## Trending Questions

**Q.**The number of integral solutions for the equation x+y+z+t=20, where x, y, z, t are all ≥−1, is

- 27C3
- 20C4
- 27C4
- 23C3

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

- 64
- 84
- 126
- 80

**Q.**The number of non negative integral solution of x1+x2+x3+4x4=20 is

- 443
- 655
- 536
- none of these

**Q.**The number of ways of distributing 20 identical fruits among 5 people, so that no one receives less than 3 fruits is

- 180
- 126
- 196
- 216

**Q.**

If x denotes the number of sixes in four consecutive throws of a dice, then P(x = 4) is

1/1296

4/6

1

1295/1296

**Q.**If x1+x2+x3+x4+x5=6, then the difference between the number of non negative integral solutions and the number of positive integral solutions will be

**Q.**In how many ways can 15 identical blankets be distributed among 6 persons such that everyone gets atleast one blanket and two particular persons get equal blankets and another three particular persons get equal blankets.

- 8
- 15
- 10
- 12

**Q.**

The number of positive integral solutions of $a\xb7b\xb7c=30$ is$?$

$30$

$27$

$8$

$6$

**Q.**

The coefficient ofx103 in (1+x+x2+x3+x4)199.(x−1)201 is

8

9

0

11

**Q.**The number of positive integral solutions of the equation x1x2x3x4x5=1050 is 375n when n∈N. Then n=

**Q.**Number of positive integral solutions of 15<x1+x2+x3≤20 is

**Q.**In how many different ways , can 3 persons A, B, C having 6 one rupee coin, 7 one rupee coin, 8 one rupee coin, respectively donate 10 one rupee coin collectively ?

- 50
- 47
- 66
- 56

**Q.**If [x] be the greatest integer less than or equal to x, then 100∑n=8[(−1)nn2] is equal to

- 2
- −2
- 0
- 4

**Q.**Fifteen identical balls have to be put in five different boxes. Each box can contain any number of balls. The total number of ways of putting the balls into the boxes so that each box contains at least two balls is equal to k. Then which of the following is/are divisor of k:

- 9
- 7
- 15
- 21

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

- 10
- 84
- 56
- None of these

**Q.**The number of non negative integral solutions for the equations a+b+c+d+e=16 and a+b+c=7 is

- 36
- 185
- 192
- 360

**Q.**The total number of positive integral solution of 15<x1+x2+x3≤20 is equal to

- 685
- 785
- 1125
- none of these

**Q.**In how many ways can 14 identical toys be distributed among 3 boys so that each one gets atleast one toy and no two boys get equal number of toys ?

- 60
- 10
- 20
- none of these

**Q.**The total number of ways of distributing 21 books among 5 children

- without any restriction is 25C4
- when each child should get atleast one book is 16C4
- when each child should get atleast three books is 10C4
- when each child should get atleast four books is 5

**Q.**In how many ways, can we get a sum greater than 17 by throwing six distinct dice

- 66−( 17C6−6 11C5)
- 66−( 17C6+6 11C5)
- 56−( 17C6−6 11C5)
- 56−( 17C6+6 11C5)

**Q.**The number of non-negative integral solutions of the equation x+y+z+5t=15 is

- 196
- 224
- 312
- 364

**Q.**

The data in the following table show that the percentage of adults in the United States who are currently married is declining.

$$\begin{array}{|cc|}\hline \text{Year}& \text{Percent of Adults}\\ \text{Who Are Married}\\ 1960& 72.2\mathrm{\%}\\ 1980& 62.3\\ 2000& 57.4\\ 2010& 51.4\\ 2012& 50.5\\ \hline\end{array}$$

Assuming that the percentage of adults who are married will continue to decrease according to the exponential decay model:

a) Use the data for $1960and2012$ to find the value of $k$ and to write an exponential function that describes the percent of adults married after time $t$, in years, where $t$ is the number of years after $1960$ .

b) Estimate the percent of adults who are married in $2015\text{andin}2018$.

c) At this decay rate, in which year will the percent of adults who are married be $40\mathrm{\%}?$

**Q.**For the equation x1+x2+x3≤13, the correct option(s) is/are

- The number of non negative integral solution will be 560
- The number of positive integral solution will be 220
- The number of non negative integral solution, when x2≥3 will be 286
- The number of non negative integral solution, when x1≥2, x2≥4 will be 120

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

- 25C4
- 12C8
- 13C3
- 14C4

**Q.**The number of integral solutions of x+y+z=0 with x≥−5, y≥−5, z≥−5 is

- 134
- 138
- 136
- 140

**Q.**Let n and k be positive integers such that n≥k+1C2 .The number of integral solutions of x1+x2+⋯+xk=n, x1≥1, x2≥2, ⋯xk≥k is

- (n−kC2)Ck
- (n−1−kC2)Ck
- (n−1−kC2)Ck−1
- (n+1−kC2)Ck−1

**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

- 56
- 75
- 90
- 105

**Q.**The number of ways of selecting 10 books from book store containing unlimited number of Physics, Chemistry, Mathematics and biology books is

**Q.**

How do you find $2A-3B$ given $A=\left[\begin{array}{cccc}5& -2& 3& 1\end{array}\right]$ and $B=\left[\begin{array}{cccc}-2& 3& 1& 0\end{array}\right]$ ?

**Q.**The number of integral solutions of the equation x+y+z+t=20, such that x≥0, y≥1, z≥2, t≥3, is

- 680
- 720
- 640
- 560