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  • Help me understand! Then number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

Then number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

  • Option 1)

    3^{8}\;

  • Option 2)

    21

  • Option 3)

    5

  • Option 4)

    \; ^{8}C_{3}

 

Answers (1)

best_answer

As we learnt in

Theorem of Number of Solutions -

Number of non-negative integral solutions of the equation x1 + x2 + x3 +......... + xr=n is ^{n+r-1}c_{n}.

- wherein

Where x_{i}\geq 0

 

 Let the number of balls in 3 boxes be x, y, z.

x + y + z = 8

(x - 1) + (y - 1) + (z - 1) = 8 - 3

x' + y' + z' = 5

Positive integral solutions are ^{5+3-1}C_{3-1}=^{7}C_{2}=\frac{7\times6}{2}=21

Correct option is 2.

 


Option 1)

3^{8}\;

This is an incorrect option.

Option 2)

21

This is the correct option.

Option 3)

5

This is an incorrect option.

Option 4)

\; ^{8}C_{3}

This is an incorrect option.

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Plabita

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