## mathmath333 one year ago 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)

1. mathmath333

\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}}

2. TylerD

um infinity?

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 ....

4. mathmath333

\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}}

5. mathmath333

i hope this is correct