(B) The problem is equivalent to finding the number of non-negative integer solutions to the equation $x_1 + x_2 + x_3 = 35$,where $x_i \ge 0$.Using t

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) The problem is equivalent to finding the number of non-negative integer solutions to the equation $x_1 + x_2 + x_3 = 35$,where $x_i \ge 0$.Using the stars and bars formula,the number of ways is given by $^{n+r-1}C_{r-1}$,where $n = 35$ and $r = 3$.Number of ways $= ^{35+3-1}C_{3-1} = ^{37}C_2$.$^{37}C_2 = \frac{37 \times 36}{2} = 37 \times 18 = 666$.

Class 11 Mathematics Permutation and Combination Definition of combinations, Condition combinations

Difficult

The number of ways in which $35$ apples can be distributed among $3$ boys so that each can have any number of apples,is

A
$1332$
B
$666$
C
$333$
D
None of these

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Permutation and Combination

Subtopic

Definition of combinations, Condition combinations

Compute $\frac{12!}{10! \times 2!}$

Easy

View Solution

An examiner can assign $30$ marks to $8$ questions. If he does not assign less than $2$ marks to any question,in how many ways can he assign the marks?

Medium

View Solution

The greatest integer which divides $(p+1)(p+2)(p+3) \ldots (p+q)$ for all $p \in N$ and fixed $q \in N$ is

EasyWBJEE 2017

View Solution

If ${}^{n-1}C_3 + {}^{n-1}C_4 > {}^{n}C_3$,then $n$ is just greater than which integer?

DifficultWBJEE 2010

View Solution

If ${}^n C_r$ denotes the number of combinations of $n$ things taken $r$ at a time,then the expression ${}^n C_{r+1} + {}^n C_{r-1} + 2{}^n C_r$ equals

MediumAIEEE 2003

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The number of ways in which $35$ apples can be distributed among $3$ boys so that each can have any number of apples,is

Similar Questions

Compute $\frac{12!}{10! \times 2!}$

An examiner can assign $30$ marks to $8$ questions. If he does not assign less than $2$ marks to any question,in how many ways can he assign the marks?

The greatest integer which divides $(p+1)(p+2)(p+3) \ldots (p+q)$ for all $p \in N$ and fixed $q \in N$ is

If ${}^{n-1}C_3 + {}^{n-1}C_4 > {}^{n}C_3$,then $n$ is just greater than which integer?

If ${}^n C_r$ denotes the number of combinations of $n$ things taken $r$ at a time,then the expression ${}^n C_{r+1} + {}^n C_{r-1} + 2{}^n C_r$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module