STD 11 - 14. probability — Maths STD 11 Science — Question

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.

$=\frac{\left({ }^{9} C _{2} \times\left(2^{5}-2\right)+{ }^{9} C _{1} \times\left(2^{4}-1\right)\right)}{9 \times 10^{4}}$

$=\frac{36 \times(32-2)+9 \times(16-1)}{9 \times 10^{4}}$

$=\frac{4 \times 30+15}{10^{4}}=\frac{135}{10^{4}}$