Mixing
In how many sequences $n$ terms long does $x$ appear?
$begingroup$
How many sequences $n$ terms long exist where each term is a number from $0$-$9$, and a specific number, let’s say $x$, is present anywhere in the sequence.
I thought to solve this by taking all the possible sequences, $10^n$, and subtracting from it the sequences where $x$ is not present, meaning $9^n$.
Is this correct?
So for a sequence $2$ terms long, there are $19$ sequences where the number $2$ appears.
combinatorics
edited Jan 22 at 13:45
Naman Kumar
22813
asked Jan 22 at 13:24
DavidDavid
284
$endgroup$
add a comment |
$begingroup$
How many sequences $n$ terms long exist where each term is a number from $0$-$9$, and a specific number, let’s say $x$, is present anywhere in the sequence.
I thought to solve this by taking all the possible sequences, $10^n$, and subtracting from it the sequences where $x$ is not present, meaning $9^n$.
Is this correct?
So for a sequence $2$ terms long, there are $19$ sequences where the number $2$ appears.
combinatorics
edited Jan 22 at 13:45
Naman Kumar
22813
asked Jan 22 at 13:24
DavidDavid
284
$endgroup$
$begingroup$
This question is nearly equivalent to asking How many $n$-digit numbers have $x$ in them? That said, your solution seems correct.
$endgroup$
– Naman Kumar
Jan 22 at 13:31
2
$begingroup$
Your solution is correct.
$endgroup$
– N. F. Taussig
Jan 22 at 13:36
add a comment |
$begingroup$
How many sequences $n$ terms long exist where each term is a number from $0$-$9$, and a specific number, let’s say $x$, is present anywhere in the sequence.
I thought to solve this by taking all the possible sequences, $10^n$, and subtracting from it the sequences where $x$ is not present, meaning $9^n$.
Is this correct?
So for a sequence $2$ terms long, there are $19$ sequences where the number $2$ appears.
combinatorics
edited Jan 22 at 13:45
Naman Kumar
22813
asked Jan 22 at 13:24
DavidDavid
284
$endgroup$
How many sequences $n$ terms long exist where each term is a number from $0$-$9$, and a specific number, let’s say $x$, is present anywhere in the sequence.
I thought to solve this by taking all the possible sequences, $10^n$, and subtracting from it the sequences where $x$ is not present, meaning $9^n$.
Is this correct?
So for a sequence $2$ terms long, there are $19$ sequences where the number $2$ appears.
combinatorics
combinatorics
edited Jan 22 at 13:45
Naman Kumar
22813
asked Jan 22 at 13:24
DavidDavid
284
edited Jan 22 at 13:45
Naman Kumar
22813
asked Jan 22 at 13:24
DavidDavid
284
edited Jan 22 at 13:45
Naman Kumar
22813
edited Jan 22 at 13:45
Naman Kumar
22813
edited Jan 22 at 13:45
Naman Kumar
22813
22813
asked Jan 22 at 13:24
DavidDavid
284
asked Jan 22 at 13:24
DavidDavid
284
asked Jan 22 at 13:24
DavidDavid
284
284
$begingroup$
This question is nearly equivalent to asking How many $n$-digit numbers have $x$ in them? That said, your solution seems correct.
$endgroup$
– Naman Kumar
Jan 22 at 13:31
2
$begingroup$
Your solution is correct.
$endgroup$
– N. F. Taussig
Jan 22 at 13:36
add a comment |
$begingroup$
This question is nearly equivalent to asking How many $n$-digit numbers have $x$ in them? That said, your solution seems correct.
$endgroup$
– Naman Kumar
Jan 22 at 13:31
2
$begingroup$
Your solution is correct.
$endgroup$
– N. F. Taussig
Jan 22 at 13:36
$begingroup$
This question is nearly equivalent to asking How many $n$-digit numbers have $x$ in them? That said, your solution seems correct.
$endgroup$
– Naman Kumar
Jan 22 at 13:31
$begingroup$
This question is nearly equivalent to asking How many $n$-digit numbers have $x$ in them? That said, your solution seems correct.
$endgroup$
– Naman Kumar
Jan 22 at 13:31
2
2
$begingroup$
Your solution is correct.
$endgroup$
– N. F. Taussig
Jan 22 at 13:36
$begingroup$
Your solution is correct.
$endgroup$
– N. F. Taussig
Jan 22 at 13:36
add a comment |
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$begingroup$
This question is nearly equivalent to asking How many $n$-digit numbers have $x$ in them? That said, your solution seems correct.
$endgroup$
– Naman Kumar
Jan 22 at 13:31
2
$begingroup$
Your solution is correct.
$endgroup$
– N. F. Taussig
Jan 22 at 13:36