The number of ways of selecting two distinct numbers from the first 15 natural numbers such that their sum is a multiple of 5, is equal to

Step-by-step solution

x + y = 5 , 10 , 15 , 20 , 25 , 30 Where x ≠ y , x , y = y , x The number of solutions of x + y = 5 is 4 2 ! The number of solutions of x + y = 10 is 9 - 1 2 ! The number of solutions of x + y = 15 is 14 2 ! The number of solutions of x + y = 20 is 11 - 1 2 ! ∵ x = 5 , 6 , … , 15 The number of solutions of x + y = 25 is 6 2 ! ∵ x = 10 , 11 , … , 15 The number of solutions of x + y = 30 is 0 ∵ x = y = 15 So, the required number of solutions = 2 + 4 + 7 + 5 + 3 + 0 = 21