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 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
$\frac{7}{14}$
$\frac{8}{14}$
$\frac{9}{14}$
$\frac{10}{14}$
Solution
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 $=\frac{18}{28}=\frac{9}{14}$