Question

How many different numbers smaller than 2.10^8
can be formed using the digits 1 and 2 only ?

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{ How many different numbers smaller than}\ 2\cdot 10^8 \hspace{.33em}\\~\\
& \normalsize \text{ can be formed using the digits 1 and 2 only} \hspace{.33em}\\~\\
& a.)\ 766 \hspace{.33em}\\~\\
& b.)\ 94 \hspace{.33em}\\~\\
& c.)\ 92 \hspace{.33em}\\~\\
& d.)\ 126 \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

Using two digits,

How many 1 digit numbers are possible ?
How many 2 digit numbers are possible ?
How many 3 digit numbers are possible ?
.
.
.
How many 8 digit numbers are possible ?

Answer 3

is this correct


\(\large \color{black}{\begin{align}
2^{1}+2^{2}+2^{3}+2^{4}+2^{5}+2^{6}+2^{7}+2^{8}=510\hspace{.33em}\\~\\
\end{align}}\)

Answer 4

right!
Next, look at 9 digit numbers. The left most digit can only be 1.
If you fix the left most digit at 1, how many numbers are possible by changing remaining 8 digits ?

Answer 5

Why is this site lagging