Question

How many integers between 100 and 1000 contain no digits other than 3, 4 or 5?

Answer 1

`\begin{gathered} \text{Integers betwe}en\text{ 100 and 1000}\Rightarrow900 \\ At\text{ 100th place is there is no 3,4,5}\Rightarrow(1,2,6,7,8,9)\Rightarrow6\text{ number} \\ At\text{ 10th place is there is no 3,4,5}\Rightarrow(0,1,2,6,7,8,9)\Rightarrow7\text{ number} \\ At\text{ 1th place is there is no 3,4,5}\Rightarrow(0,1,2,6,7,8,9)\Rightarrow7\text{ number} \\ So,\text{ the integers is}\Rightarrow6*7*7=294\text{ number} \end{gathered}`