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The number of subsets of $\{1,2,3, \ldots, 9\}$ containing at least one odd number is
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The correct answer is:
496
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]
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]
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