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14. probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS14. probability1 Mark
MCQ
The probability that a randomly chosen $5-digit$ number is made from exactly two digits is
  • A
    $\frac{121}{10^{4}}$
  • B
    $\frac{150}{10^{4}}$
  • ✓
    $\frac{135}{10^{4}}$
  • D
    $\frac{134}{10^{4}}$
✓

Answer

Correct option: C.
$\frac{135}{10^{4}}$
c
First Case: Choose two non-zero digits ${ }^{9} C _{2}$

Now, number of 5 -digit numbers containing both digits $=2^{5}-2$

Second Case: Choose one non-zero \& one zero as digit ${ }^{9} C _{1}$

Number of 5 -digit numbers containg one non zero and one zero both $=\left(2^{4}-1\right)$ Required prob.

$=\frac{\left({ }^{9} C _{2} \times\left(2^{5}-2\right)+{ }^{9} C _{1} \times\left(2^{4}-1\right)\right)}{9 \times 10^{4}}$

$=\frac{36 \times(32-2)+9 \times(16-1)}{9 \times 10^{4}}$

$=\frac{4 \times 30+15}{10^{4}}=\frac{135}{10^{4}}$

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