Question

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

• A. 324
• B. 396
• C. 496
• D. 512

Answer 1

Answer: (C)

496

Answer 2

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]