The probability that a randomly chosen $5-digit$ number is made from exactly two digits is : Option: 1 Option: 2  Option: 3  Option: 4

$\\\text{First Case : Choose two non-zero digits }{ }^{9} \mathrm{C}_{2}\\\text{ Now, number of 5 -digit numbers containing both digits} =2^{5}-2\\\text{ Second Case : Choose one non-zero and one zero as digit} { }^{9} \mathrm{C}_{1}.\\\text{ Number of 5 -digit numbers containing one non zero and one zero both}=\left(2^{4}-1\right)\\\text{ Required prob.}$

$\\=\frac{\left({ }^{9} \mathrm{C}_{2} \times\left(2^{5}-2\right)+{ }^{9} \mathrm{C}_{1} \times\left(2^{4}-1\right)\right)}{9 \times 10^{4}} \\ =\frac{36 \times(32-2)+9 \times(16-1)}{9 \times 10^{4}} \\ =\frac{4 \times 30+15}{10^{4}}=\frac{135}{10^{4}} \\$

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