## mathmath333 one year ago How many natural numbers not more than 4300 can be formed with the digits 0,1,2,3,4 (if repetitions are not allowed

1. mathmath333

\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}}

2. mathmate

0001 to 3421 = 4*4*3*2-1=95 4012 to 4300(excluded) = 1*3*3*2=18 Total 95+18=113

3. mathmath333

4. mathstudent55

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

5. mathmath333

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

6. mathmate

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.

7. mathmath333

thnks