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 $2^9=512$ Case I When selecting only one even number $\{2,4,6,8\}$ Number of ways $={ }^4 C_1=4$ 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]