Question

The probability that a randomly chosen 5 -digit number is made from exactly two digits is :

• A. $\frac{121}{10^4}$
• B. $\frac{150}{10^4}$
• C. $\frac{135}{10^4}$
• D. $\frac{134}{10^4}$

Answer 1

Answer: (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
$=\frac{\left({}^9{C}_2\times \left(2^5-2\right)+{}^9{C}_1\times \left(2^4-1\right)\right)}{9\times 10^4}$
$=\frac{36\times (32-2)+9\times (16-1)}{9\times 10^4}$
$=\frac{4\times 30+15}{10^4}=\frac{135}{10^4}$