The number of ways in which three numbers in arithmetic progression can be selected from 1 , 2 , 3 , … … , 50 is

Step-by-step solution

a + c = 2 b So, both a and c will be even or both will be odd as their sum is even. In first 50 natural number 25 are even and 25 are odd. Required number of ways 2 C 52 + 2 C 52 = 2 × 25 × 24 2 = 600