A set of five distinct digits is given as S = 1, 2, 4, 5, d , where d is a single-digit non-negative integer. It is known that exactly 36 three-digit numbers strictly greater than 400 can be formed using the digits from S without repetition. The sum of all possible values of d is

Step-by-step solution

For a 3 -digit number to be strictly greater than 400 , its hundreds digit must be 4 or greater. Case 1: If d The possible hundreds digits are 4 and 5 ( 2 choices). The remaining two positions can be filled by the remaining 4 digits in ⁴P₂ = 4 3 = 12 ways. Total numbers formed = 2 12 = 24 . This contradicts the given condition that 36 such numbers can be formed. Case 2: If d > 4 The possible hundreds digits are 4, 5, and d ( 3 choices). The remaining two positions can be filled in 4 3 = 12 ways. Total numbers forme