question_answer

If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is: [JEE MAIN Held on 09-01-2020 Evening]

A) \[\frac{945}{{{2}^{10}}}\]

B) \[\frac{965}{{{2}^{11}}}\]

C) \[\frac{965}{{{2}^{10}}}\]      

D) \[\frac{945}{{{2}^{11}}}\]

Correct Answer: A

Solution :

Total ways of distribution \[={{4}^{10}}={{2}^{20}}\] Favourable ways Required probability \[=\frac{6\cdot 252\cdot \,10\,\cdot \,2\,\cdot \,{{2}^{5}}}{{{2}^{20}}}\]                         \[=\frac{3\times 63\times 5}{{{2}^{10}}}=\frac{945}{{{2}^{10}}}\]