Question

If two different numbers are taken from the set $\\{0,1,2,3, \ldots \ldots, 10\\}$then the probability that their sum as well as absolute difference are both multiple of $4$, is :

• A. $\frac{12}{55}$
• B. $\frac{14}{45}$
• C. $\frac{7}{55}$
• D. $\frac{6}{55}$

Answer 1

Answer: (D)

$\frac{6}{55}$

Answer 2

Total number of ways $={ }^{11} C_{2}$
$=55$
Favourable ways are
$(0,4),(0,8),(4,8),(2,6),(2,10),(6,10)$
Probability $=\frac{6}{55}$