Question

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

• A. 324
• B. 396
• C. 496
• D. 512

Answer 1

The Correct Option is C

The total number of subsets of given set is $2^{9}=512$
When selecting only one even number $\{2,4,6,8\}$
Number of ways $={ }^{4} C_{1}=4$
When selecting only two even numbers $={ }^{4} C_{2}=6$
When selecting only three even numbers $={ }^{4} C_{3}=4$
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]