mathmath333
  • mathmath333
How many natural numbers not more than 4300 can be formed with the digits 0,1,2,3,4 (if repetitions are not allowed
Mathematics
chestercat
  • chestercat
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{ How many natural numbers not more than 4300}\hspace{.33em}\\~\\ & \normalsize \text{ can be formed with the digits 0,1,2,3,4}\hspace{.33em}\\~\\ & \normalsize \text{ (if repetitions are not allowed)}\hspace{.33em}\\~\\ & a.)\ 113 \hspace{.33em}\\~\\ & b.)\ 158 \hspace{.33em}\\~\\ & c.)\ 154 \hspace{.33em}\\~\\ & d.)\ 119 \hspace{.33em}\\~\\ \end{align}}\)
mathmate
  • mathmate
0001 to 3421 = 4*4*3*2-1=95 4012 to 4300(excluded) = 1*3*3*2=18 Total 95+18=113
mathmath333
  • mathmath333
answer given is b.) 158

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mathstudent55
  • 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
mathmath333
  • 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
mathmate
  • 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.
mathmath333
  • mathmath333
thnks

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