Two numbers are chosen at random from $\{1,2,3,4,5,6,7,8\}$ at a time. The probability that smaller of the two numbers is less than 4 is

Case I When smaller of the two numbers is 1. Then, total number of cases $$ =1 \times{ }^7 C_1=7 $$ Case II When smaller of two numbers is 2 . Then, total number of cases $$ =1 \times{ }^6 C_1=6 $$ Case III When smaller of two numbers is 3 . Then, total number of cases $$ =1 \times{ }^5 C_1=5 $$ Total favourable cases $=7+6+5=18$ Total case $={ }^8 \mathrm{C}_2=28$ $\therefore \quad$ Required probability $=\frac{18}{28}=\frac{9}{14}$