The number of subsets of $\{1,2,3, \ldots, 9\}$ containing at least one odd number is

The total number of subsets of given set is $2^{9}=512$ Even numbers are $\{2,4,6,8\}$. Case I : When selecting only one even number $={ }^{4} C_{1}=4$ Case II : When selecting only two even numbers $={ }^{4} C_{2}=6$ Case III : When selecting only three even numbers $={ }^{4} C_{3}=4$ Case IV : When selecting only four even numbers $={ }^{4} C_{4}=1$ $\therefore$ Required number of ways $$ =512-(4+6+4+1)-1=496 $$ [Here, we subtract 1 for due to the null set]