JEE Mains · Maths · STD 11 - 14. probability
If \(12\) identical balls are to be placed in \(3\) identical boxes, then the probability that one of the boxes contains exactly \(3\) balls is :
- A \(22{\left( {\frac{1}{3}} \right)^{11}}\)
- B \(\frac{{55}}{3}{\left( {\frac{2}{3}} \right)^{11}}\)
- C \(55{\left( {\frac{2}{3}} \right)^{10}}\)
- D \(220{\left( {\frac{1}{3}} \right)^{12}}\)
Answer & Solution
Correct Answer
(B) \(\frac{{55}}{3}{\left( {\frac{2}{3}} \right)^{11}}\)
Step-by-step Solution
Detailed explanation
\(x + y = 9\) \(P{ = ^9}{C_3}{\left( {\frac{1}{3}} \right)^3}{\left( {\frac{2}{3}} \right)^9}\) \( = \frac{{12 \times 11 \times 10}}{3} \times \frac{1}{{{3^3}}} \times {\left( {\frac{2}{3}} \right)^9}\) \( = \frac{{220}}{{{3^3}}} \times {\left( {\frac{2}{3}} \right)^9}\)…
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