Introduction to probability

Question

The probability that when 12 distinct balls are distributed among three boxes, the first will contain exactly three balls is

Moderate

Solution

3 balls for 1^{st} Box can be selected in ${}^{12}{\mathrm{C}}_{3}$ ways, remaining 9 balls can be placed in remaining 2 boxes in 2^{9} ways.

Number of favourable cases ${=}^{12}{\mathrm{C}}_{3}\times {2}^{9}$

Total number of cases = 3^{12}

Required Probability $=\frac{{}^{12}{\mathrm{C}}_{3}\times {2}^{9}}{{3}^{12}}=\frac{{}^{12}{\mathrm{C}}_{3}\times {2}^{9}}{{9}^{6}}$

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