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Q. The probability, that in a randomly selected $3$-digit number at least two digits are odd, is

JEE MainJEE Main 2022Probability - Part 2

Solution:

At least two digits are odd
= exactly two digits are odd + exactly there 3 digits
are odd
For exactly three digits are odd
image
For exactly two digits odd :
If 0 is used then $: 2 \times 5 \times 5=50$
If 0 is not used then $:{ }^{3} C_{1} \times 4 \times 5 \times 5=300$
Required Probability $=\frac{475}{900}=\frac{19}{36}$