Question:
The probability that a randomly chosen 5 -digit number is made from exactly two digits is :
Correct Option: 1
Solution:
Total outcomes $=9\left(10^{4}\right)$
Favourable outcomes
$={ }^{9} C_{2}\left(2^{5}-2\right)+{ }^{9} C_{1}\left(2^{4}-1\right)=36(30)+9(15)$
Probability $=\frac{36 \times 30+9 \times 15}{9 \times 10^{4}}=\frac{4 \times 30+15}{10^{4}}=\frac{135}{10^{4}}$
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