A bag contains 30 tokens numbered serially from 0 to 29 . The number of ways of choosing 3 tokens from the bag, such that the sum on them is 30 , is

Step-by-step solution

Let, a , b , c be the selected numbers; a + b + c = 30 ;   a < b < c . a = 0 ⇒ b , c = 1,29 2,28 . . . . . 14,16 → Total   14   ways . a = 1 ⇒ b , c = 2,27 3,26 . . . . . 14,15 → Total   13   ways . a = 2 ⇒ b , c = 3,25 4,24 . . . . . 13,15 → Total   11   ways . a = 3 ⇒ b , c = 4,23 5,22 . . . . . 13,14 → Total   10   ways . a = 4 ⇒ b , c = 5,21 6,20 . . . . . 12,14 → Total   8   ways . a = 5 &