A box contain a certain number of balls, marked successively from 1 to n. If there are 55 different ways that two balls can be selected from the box such that the ball with number 3 marked on it is not selected, then what is the value of n?  Pick
A) 6  B) 8  C) 9  D) 12  E) 14
Total ways of selecting 2 balls out of n balls = nC2   We're told that one balls marked as 3 cannot be selected.   So total number of balls left now = (n-1)   Hence total ways of selecting 2 balls out of (n-1) balls = (n-1)C2   Given that (n-1)C2 = 55   So, [(n-1)(n-2)]/[2 * 1] = 55   So, n^2-3n+2 = 110   So, n^2-3n-108 = 0   So, n = 12 or -9 (rejected)   Hence option 4.   ANSWER:12
<result>D</result>
A box contain a certain number of balls, marked successively from 1 to n. If there are 55 different ways that two balls can be selected from the box such that the ball with number 3 marked on it is not selected, then what is the value of n?