How many 5 digit numbers contain the sequence “12”
$begingroup$
Searched elsewhere to try to answer this but I'm still confused. Note that "12" can occur more than once, we just want numbers where it occurs at least once.
My best attempt (but I think I'm double counting):
$xx(10)(10)(10)$ OR $(10)xx(10)(10)$ OR $(10)(10)xx(10)$ OR $(10)(10)(10)xx$
"xx" means the two digit options are already filled (by "12"). So in total $4(10^3)$
Can someone walk me through how to think about this?
combinatorics
$endgroup$
add a comment |
$begingroup$
Searched elsewhere to try to answer this but I'm still confused. Note that "12" can occur more than once, we just want numbers where it occurs at least once.
My best attempt (but I think I'm double counting):
$xx(10)(10)(10)$ OR $(10)xx(10)(10)$ OR $(10)(10)xx(10)$ OR $(10)(10)(10)xx$
"xx" means the two digit options are already filled (by "12"). So in total $4(10^3)$
Can someone walk me through how to think about this?
combinatorics
$endgroup$
1
$begingroup$
What about $1212x$ and $x1212$ and $12x12$?
$endgroup$
– kingW3
Dec 13 '18 at 16:07
$begingroup$
I see, so maybe then it'd be $4(10^3) + 3(10)$ ?
$endgroup$
– user609600
Dec 13 '18 at 16:12
add a comment |
$begingroup$
Searched elsewhere to try to answer this but I'm still confused. Note that "12" can occur more than once, we just want numbers where it occurs at least once.
My best attempt (but I think I'm double counting):
$xx(10)(10)(10)$ OR $(10)xx(10)(10)$ OR $(10)(10)xx(10)$ OR $(10)(10)(10)xx$
"xx" means the two digit options are already filled (by "12"). So in total $4(10^3)$
Can someone walk me through how to think about this?
combinatorics
$endgroup$
Searched elsewhere to try to answer this but I'm still confused. Note that "12" can occur more than once, we just want numbers where it occurs at least once.
My best attempt (but I think I'm double counting):
$xx(10)(10)(10)$ OR $(10)xx(10)(10)$ OR $(10)(10)xx(10)$ OR $(10)(10)(10)xx$
"xx" means the two digit options are already filled (by "12"). So in total $4(10^3)$
Can someone walk me through how to think about this?
combinatorics
combinatorics
asked Dec 13 '18 at 16:00
user609600
1
$begingroup$
What about $1212x$ and $x1212$ and $12x12$?
$endgroup$
– kingW3
Dec 13 '18 at 16:07
$begingroup$
I see, so maybe then it'd be $4(10^3) + 3(10)$ ?
$endgroup$
– user609600
Dec 13 '18 at 16:12
add a comment |
1
$begingroup$
What about $1212x$ and $x1212$ and $12x12$?
$endgroup$
– kingW3
Dec 13 '18 at 16:07
$begingroup$
I see, so maybe then it'd be $4(10^3) + 3(10)$ ?
$endgroup$
– user609600
Dec 13 '18 at 16:12
1
1
$begingroup$
What about $1212x$ and $x1212$ and $12x12$?
$endgroup$
– kingW3
Dec 13 '18 at 16:07
$begingroup$
What about $1212x$ and $x1212$ and $12x12$?
$endgroup$
– kingW3
Dec 13 '18 at 16:07
$begingroup$
I see, so maybe then it'd be $4(10^3) + 3(10)$ ?
$endgroup$
– user609600
Dec 13 '18 at 16:12
$begingroup$
I see, so maybe then it'd be $4(10^3) + 3(10)$ ?
$endgroup$
– user609600
Dec 13 '18 at 16:12
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Guide:
Let $A$ denote the set of $5$-digit numbers of the form $12***$.
Let $B$ denote the set of $5$-digit numbers of the form $*12**$.
Let $C$ denote the set of $5$-digit numbers of the form $**12*$.
Let $D$ denote the set of $5$-digit numbers of the form $***12$.
Then to be found is $|Acup Bcup Ccup D|$ and this can be done using the principle of inclusion/exclusion.
answered Dec 13 '18 at 16:13
drhabdrhab
104k545136
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3038199%2fhow-many-5-digit-numbers-contain-the-sequence-12%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Guide:
Let $A$ denote the set of $5$-digit numbers of the form $12***$.
Let $B$ denote the set of $5$-digit numbers of the form $*12**$.
Let $C$ denote the set of $5$-digit numbers of the form $**12*$.
Let $D$ denote the set of $5$-digit numbers of the form $***12$.
Then to be found is $|Acup Bcup Ccup D|$ and this can be done using the principle of inclusion/exclusion.
answered Dec 13 '18 at 16:13
drhabdrhab
104k545136
$endgroup$
add a comment |
$begingroup$
Guide:
Let $A$ denote the set of $5$-digit numbers of the form $12***$.
Let $B$ denote the set of $5$-digit numbers of the form $*12**$.
Let $C$ denote the set of $5$-digit numbers of the form $**12*$.
Let $D$ denote the set of $5$-digit numbers of the form $***12$.
Then to be found is $|Acup Bcup Ccup D|$ and this can be done using the principle of inclusion/exclusion.
answered Dec 13 '18 at 16:13
drhabdrhab
104k545136
$endgroup$
add a comment |
$begingroup$
Guide:
Let $A$ denote the set of $5$-digit numbers of the form $12***$.
Let $B$ denote the set of $5$-digit numbers of the form $*12**$.
Let $C$ denote the set of $5$-digit numbers of the form $**12*$.
Let $D$ denote the set of $5$-digit numbers of the form $***12$.
Then to be found is $|Acup Bcup Ccup D|$ and this can be done using the principle of inclusion/exclusion.
answered Dec 13 '18 at 16:13
drhabdrhab
104k545136
$endgroup$
Guide:
Let $A$ denote the set of $5$-digit numbers of the form $12***$.
Let $B$ denote the set of $5$-digit numbers of the form $*12**$.
Let $C$ denote the set of $5$-digit numbers of the form $**12*$.
Let $D$ denote the set of $5$-digit numbers of the form $***12$.
Then to be found is $|Acup Bcup Ccup D|$ and this can be done using the principle of inclusion/exclusion.
answered Dec 13 '18 at 16:13
drhabdrhab
104k545136
answered Dec 13 '18 at 16:13
drhabdrhab
104k545136
answered Dec 13 '18 at 16:13
drhabdrhab
104k545136
answered Dec 13 '18 at 16:13
drhabdrhab
104k545136
104k545136
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3038199%2fhow-many-5-digit-numbers-contain-the-sequence-12%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
$begingroup$
What about $1212x$ and $x1212$ and $12x12$?
$endgroup$
– kingW3
Dec 13 '18 at 16:07
$begingroup$
I see, so maybe then it'd be $4(10^3) + 3(10)$ ?
$endgroup$
– user609600
Dec 13 '18 at 16:12