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STD 11 - 14. probability — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. probability4 Marks
MCQ
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 
  • A
    $\frac{945}{2^{11}}$
  • B
    $\frac{965}{2^{11}}$
  • ✓
    $\frac{945}{2^{10}}$
  • D
    $\frac{965}{2^{10}}$
✓

Answer

Correct option: C.
$\frac{945}{2^{10}}$
c
Total ways $=4^{10}=\mathrm{n}$

Number of ways placing exactly 2 and 3 balls

in two of these boxes $=^{4} \mathrm{C}_{2} \times \frac{ 5!}{ 2! {3!}} \times 2! \times^{10} \mathrm{C}_{5} \times 2^{5}=\mathrm{m}$

Required probability $=\frac{\mathrm{m}}{\mathrm{n}}=\frac{945}{2^{10}}$

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