The number of subsets of $\{1,2,3, \ldots, 9\}$ containing at least one odd number is
The number of subsets of $\{1,2,3, \ldots, 9\}$ containing at least one odd number is
324
396
496
512
Solution
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]