Question

Amartya Banerjee has forgotten the telephone number
of his best friend Abhijit Roy. All he remembers is that
the number had 8-digits and ended with an odd number
and had exactly one nine . How many possible numbers
does Amartya have to try to be sure that he gets
correct number ?

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{ Amartya Banerjee has forgotten the telephone number }\hspace{.33em}\\~\\
& \normalsize \text{ of his best friend Abhijit Roy. All he remembers is that }\hspace{.33em}\\~\\
& \normalsize \text{ the number had 8-digits and ended with an odd number }\hspace{.33em}\\~\\
& \normalsize \text{ and had exactly one nine . How many possible numbers}\hspace{.33em}\\~\\
& \normalsize \text{ does Amartya have to try to be sure that he gets}\hspace{.33em}\\~\\
& \normalsize \text{ correct number ?}\hspace{.33em}\\~\\
& a.)\ 104\cdot 9^{5} \hspace{.33em}\\~\\
& b.)\ 113\cdot 9^{5} \hspace{.33em}\\~\\
& c.)\ 300\cdot 9^{5} \hspace{.33em}\\~\\
& d.)\ 764\cdot 9^{5}\cdot 6! \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

lets take cases :)

case 1-
9 at the end

now 9 at 1st->

now for 9 at 2nd/3rd/4th/5th/6th/7th place->
lets take 9 at 2