Question

The number of ways in which three distinct number in AP can be selected from the set {1, 2, 3 . . . .24} is equal to

• A. 66
• B. 132
• C. 198
• D. 276

Answer 1

The correct option is B 132

Let the number selected be $2x_2=x_1+x_3$
i.e., $x_1,x_3$ is even ${\Rightarrow }^{12}{C}_2$
$x_1,x_3$ is odd ${\Rightarrow }^{12}{C}_2$
132 ways