Question

How many natural numbers not more than 4300
can be formed with the digits 0,1,2,3,4
(if repetitions are allowed)

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{ How many natural numbers not more than 4300}\hspace{.33em}\\~\\
& \normalsize \text{ can be formed with the digits 0,1,2,3,4}\hspace{.33em}\\~\\
& \normalsize \text{ (if repetitions are allowed)}\hspace{.33em}\\~\\
& a.)\ 574 \hspace{.33em}\\~\\
& b.)\ 570 \hspace{.33em}\\~\\
& c.)\ 575 \hspace{.33em}\\~\\
& d.)\ 569 \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

Using regex notation and abbreviating [01234] as []
Note: [01234] means choose one digit out of {0,1,2,3,4}

[0123][][][] = 4*5^3
-[0][0][0][0] = -1
[4][012][[][] = 1*3*5^2
[4][0][0][0] = 1

total = 500-1+75+1=575 (if natural number defined as {1,2,3,4.....}]

Answer 3

*[4][3][0][0] = 1

Answer 4

i m not getting this notation

Answer 5

\(\large \color{black}{\begin{align}
& 5^{4}-1-(2\times 5^{2} -1)=575 \hspace{.33em}\\~\\
\end{align}}\)

Answer 6

Yes, you can do that too!