VITEEE 2009 Paper

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 = ${}^{4}C_{4}=1$ ∴ Required number of ways = 512 - (4 + 6 + 4 + 1) - 1 = 496 [Here, we subtract 1 for due to the null set.]