How many integers between 1000 and 10000 have
no digits other than 4, 5 or 6?  Pick
A) 91  B) 51  C) 81  D) 71  E) 61

Rationale: any number between 1000 and 10000 is of 4 digits . the unit ’ s place can be filled up by 45 or 6 , that is , in 3 ways . similarly , the ten ’ s place can be filled up by 4 or 5 or 6 , that is in 3 ways . the hundred ’ s place can be filled up by 4 , 5 or 6 , that is in 3 ways and the thousand ’ s place can . be filled up by 4 or 5 or 6 , that is , in 3 ways . hence the required numbers = 3 x 3 x 3 x 3 = 81 answer : c
Answer: C