Question

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

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{ How many natural numbers not more than 4300}\hspace{.33em}\\~\\
& \normalsize \text{ can be formed with the digits 0,1,2,3,4}\hspace{.33em}\\~\\
& \normalsize \text{ (if repetitions are not allowed)}\hspace{.33em}\\~\\
& a.)\ 113 \hspace{.33em}\\~\\
& b.)\ 158 \hspace{.33em}\\~\\
& c.)\ 154 \hspace{.33em}\\~\\
& d.)\ 119 \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

0001 to 3421 = 4*4*3*2-1=95
4012 to 4300(excluded) = 1*3*3*2=18

Total 95+18=113

Answer 3

answer given is b.) 158

Answer 4

1-digit numbers: 1, 2, 3, 4: 4 numbers

2-digit numbers: 4 * 4 = 16

3-digit numbers: 4 * 4 * 3 = 48

4-digit numbers: Starting with 1, 2, 3: 3 * 4 * 3 * 2 = 72

4-digit number: Starting with 4:
4012, 4021, 4102, 4120, 4201, 4210,
4013, 4031, 4103, 4130,
4023, 4032, 4023, 4230,
4123, 4132, 4213, 4231: 18 numbers

Total: 4 + 16 + 48 + 72 + 18 = 158 numbers

Answer 5

how can one find this without listing it.

4-digit number: Starting with 4:
4012, 4021, 4102, 4120, 4201, 4210,
4013, 4031, 4103, 4130,
4023, 4032, 4023, 4230,
4123, 4132, 4213, 4231: 18 numbers

Answer 6

Yep, I overlooked that fact that leading zeroes can be repeated! thank you @mathstudent55

we have 1 choice for digit 1 {4}
3 choices for digit 2 {0,1,2}
3 remaining choices for digit 3
2 remaining choices for digit 4
for a total of 1*3*3*2=18 numbers.

Answer 7

thnks