howmany 3 digit numbers are there tens digit place is more than hundreds digit place and units place less than hundreds digit place?  Choose the correct choice from the following choices.
A) 80	B) 100	C) 110	D) 120	E) 140

Rationale: we have numbers { 01 , 23 , 45 , 67 , 89 } now we would decide the cases on behalf of value of hundred place digit . and accordingly choose unit ' s digit and ten ' s digit . value of hundred place digit must be choosen in such a manner that there should exist a greater digit for ten ' s place and a smaller digit for unit place . thus we can have values of hundred ' s digit from 12 , 34 , 56 , 78 only now starting from hundred ' s digit = 8 : hundred ' s digit possible values for ten ' s digit possible values for unit digit total ways 8 9 01 , 23 , 45 , 67 1 * 1 * 8 = 8 7 89 0 , 12 , 34 , 56 1 * 2 * 7 = 14 6 7 , 89 01 , 23 , 45 1 * 3 * 6 = 18 5 67 , 89 0 , 12 , 34 1 * 4 * 5 = 20 4 5 , 67 , 89 01 , 23 1 * 5 * 4 = 20 3 45 , 67 , 89 0 . 1.2 1 * 6 * 3 = 18 2 3 , 45 , 67 , 89 01 1 * 7 * 2 = 14 1 23 , 45 , 67 , 89 0 1 * 8 * 1 = 8 so , total no of cases = 8 + 14 + 18 + 20 + 20 + 18 + 14 + 8 = 120 hence total no of possible 3 digit numbers = 120 answer : d
Answer: D