(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

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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

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

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Permutation and Combination

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Definition of combinations, Condition combinations

Determine the number of $5$-card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.

Medium

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If ${ }^{n-3} C_r + B \cdot { }^{n-3} C_{r-1} + B^{\prime} \cdot { }^{n-3} C_{r-2} + { }^{n-3} C_{r-3} = { }^n C_r$ holds for all $n \geq r \geq 3$,then $(B, B^{\prime}) = $.

DifficultAP EAMCET 2022

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The number of ways in which any four letters can be selected from the word '$CORGOO$' is

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If $N(n) = n \prod_{r=1}^{2023} (n^2 - r^2)$ for $n > 2023$,then find the value of ${}^{N}C_{N-1}$ when $n = 2024$.

MediumAP EAMCET 2023

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What is the total number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are the $4$ cards of the same colour?

Medium

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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

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Determine the number of $5$-card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.

If ${ }^{n-3} C_r + B \cdot { }^{n-3} C_{r-1} + B^{\prime} \cdot { }^{n-3} C_{r-2} + { }^{n-3} C_{r-3} = { }^n C_r$ holds for all $n \geq r \geq 3$,then $(B, B^{\prime}) = $.

The number of ways in which any four letters can be selected from the word '$CORGOO$' is

If $N(n) = n \prod_{r=1}^{2023} (n^2 - r^2)$ for $n > 2023$,then find the value of ${}^{N}C_{N-1}$ when $n = 2024$.

What is the total number of ways of choosing $4$ cards from a pack of $52$ playing cards? In how many of these are the $4$ cards of the same colour?

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