Question

Sam has forgotten his friend’s seven-digit telephone number.
He remembers the following: the first three digits are either
635 or 674, the number is odd, and the number 9 appears
once. If Sam were to use a trial and error process to reach
his friend, what is the minimum number of trials he has to
make before he can be certain to succeed?

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{ Sam has forgotten his friend’s seven-digit telephone number.}\hspace{.33em}\\~\\
& \normalsize \text{ He remembers the following: the first three digits are either}\hspace{.33em}\\~\\
& \normalsize \text{ 635 or 674, the number is odd, and the number 9 appears }\hspace{.33em}\\~\\
& \normalsize \text{ once. If Sam were to use a trial and error process to reach }\hspace{.33em}\\~\\
& \normalsize \text{ his friend, what is the minimum number of trials he has to }\hspace{.33em}\\~\\
& \normalsize \text{ make before he can be certain to succeed?}\hspace{.33em}\\~\\
& a.)\ 1000 \hspace{.33em}\\~\\
& b.)\ 2430 \hspace{.33em}\\~\\
& c.)\ 3402 \hspace{.33em}\\~\\
& d.)\ 3006 \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

r ut yping

Answer 3

he had to make combinations like -

1)number starting with635

1st we take the case where the number has 9 at the end and calculate possibilities
nd then u take cases with 1,3,5,7 and fix 9 at one of these points- and calculate the possibilities nd then multiply it by 3 cause there are 3 such places :) so this way u get possibilities in this case :P similarly do it with 674 :)