The probability that a randomly chosen 5-digit number is made from exactly two digits is :
Correct Option: , 3
First Case: Choose two non-zero digits ${ }^{9} \mathrm{C}_{2}$
Now, number of 5 -digit numbers containing both digits $=2^{5}-2$
Second Case: Choose one non-zero \& one zero as digit ${ }^{9} \mathrm{C}_{1}$
Number of 5 -digit numbers containg one
non zero and one zero both $=\left(2^{4}-1\right)$
Required prob.
$=\frac{\left({ }^{9} \mathrm{C}_{2} \times\left(2^{5}-2\right)+{ }^{9} \mathrm{C}_{1} \times\left(2^{4}-1\right)\right)}{9 \times 10^{4}}$
$=\frac{36 \times(32-2)+9 \times(16-1)}{9 \times 10^{4}}$
$=\frac{4 \times 30+15}{10^{4}}=\frac{135}{10^{4}}$
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