(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

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(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

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Class 11 Questions

Class 11

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Chapter

Permutation and Combination

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Definition of combinations, Condition combinations

$A$ committee of $7$ members is to be formed from $9$ boys and $4$ girls. In how many ways can this be done if the committee must consist of exactly $3$ girls?

Medium

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If $^nC_{15} = ^nC_8$,then what is the value of $^nC_{21}$?

Easy

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The number of ways in which an examiner can assign $30$ marks to $8$ questions,awarding not less than $2$ marks to any question is

Difficult

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If $\binom{a^2+a}{3} = \binom{a^2+a}{9}$,then $a = \dots$

Easy

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If $\frac{1}{{ }^{5}C_{r}} + \frac{1}{{ }^{6}C_{r}} = \frac{1}{{ }^{4}C_{r}},$ then the value of $r$ is

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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

$A$ committee of $7$ members is to be formed from $9$ boys and $4$ girls. In how many ways can this be done if the committee must consist of exactly $3$ girls?

If $^nC_{15} = ^nC_8$,then what is the value of $^nC_{21}$?

The number of ways in which an examiner can assign $30$ marks to $8$ questions,awarding not less than $2$ marks to any question is

If $\binom{a^2+a}{3} = \binom{a^2+a}{9}$,then $a = \dots$

If $\frac{1}{{ }^{5}C_{r}} + \frac{1}{{ }^{6}C_{r}} = \frac{1}{{ }^{4}C_{r}},$ then the value of $r$ is

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