Question

How many even natural numbers divisible by 5
can be formed with digits 0,1,2,3,4,5,6
(if repetition is not allowed)

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{ How many even natural numbers divisible by 5}\hspace{.33em}\\~\\
& \normalsize \text{ can be formed with digits 0,1,2,3,4,5,6}\hspace{.33em}\\~\\
& \normalsize \text{ (if repetition is not allowed)}\hspace{.33em}\\~\\
& a.)\ 1957 \hspace{.33em}\\~\\
& b.)\ 1956 \hspace{.33em}\\~\\
& c.)\ 1236 \hspace{.33em}\\~\\
& d.)\ 1235 \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

um infinity?

Answer 3

its not infinity since reptition is not allowed...

the last digit has to be either 0 or 5 to be divisible by 5. since it also has to be even the only number that can be finished with is 0

so now the last digit is fixed to 0

there are 6 more digits that can be used to form 1,2,3,4,5,6 digit number plus 0 the last dgit
1digit + 0 -> 6
2digits + 0 -> 6.5
....

Answer 4

\(\large \color{black}{\begin{align}
\text{0} & \rightarrow 0 \hspace{.33em}\\~\\
\text{ _.0} & \rightarrow 6 \hspace{.33em}\\~\\
\text{ _._.0} & \rightarrow 30 \hspace{.33em}\\~\\
\text{ _._._.0} & \rightarrow 120 \hspace{.33em}\\~\\
\text{ _._._._.0} & \rightarrow 360 \hspace{.33em}\\~\\
\text{ _._._._._.0} & \rightarrow 720 \hspace{.33em}\\~\\
\text{ _._._._._._.0} & \rightarrow 720 \hspace{.33em}\\~\\
total & =1956 \hspace{.33em}\\~\\
\end{align}}\)

Answer 5

i hope this is correct