Teachers and Students sitting in a line with a condition
A class consists of three teachers (Mr. P, Ms. Q, Ms. R) and six students (Ali, Bob, Cal, Dee, Amy, Fay). How many ways can they sit in a line of 9 chairs if we have the property that between any two teachers there are exactly two students?
The correct answer is supposed to be 12,960 ways, but I cannot determine this answer. My main assumption is that there are three teachers, the two of these students will have to sit alone on the sides of the teachers. Like so:
S T S S T S S T S
My attempt:
$6times3times5times4times2times3times2times1times1$ which equals $4320$.
combinatorics
asked Nov 26 '18 at 18:40
Ludwigthestud
908
add a comment |
A class consists of three teachers (Mr. P, Ms. Q, Ms. R) and six students (Ali, Bob, Cal, Dee, Amy, Fay). How many ways can they sit in a line of 9 chairs if we have the property that between any two teachers there are exactly two students?
The correct answer is supposed to be 12,960 ways, but I cannot determine this answer. My main assumption is that there are three teachers, the two of these students will have to sit alone on the sides of the teachers. Like so:
S T S S T S S T S
My attempt:
$6times3times5times4times2times3times2times1times1$ which equals $4320$.
combinatorics
asked Nov 26 '18 at 18:40
Ludwigthestud
908
2
You can also have SSTSSTSST or TSSTSSTSS.
– JMoravitz
Nov 26 '18 at 18:41
Well, I'll be damned. My mind locked me into thinking that every two students needed a teacher to the left and right of them, but it was okay if there was lone students. I made the question harder than it needed to be.
– Ludwigthestud
Nov 26 '18 at 18:45
2
@Ludwigthestud: that gives you exactly the missing factor $3$
– Ross Millikan
Nov 26 '18 at 18:51
add a comment |
A class consists of three teachers (Mr. P, Ms. Q, Ms. R) and six students (Ali, Bob, Cal, Dee, Amy, Fay). How many ways can they sit in a line of 9 chairs if we have the property that between any two teachers there are exactly two students?
The correct answer is supposed to be 12,960 ways, but I cannot determine this answer. My main assumption is that there are three teachers, the two of these students will have to sit alone on the sides of the teachers. Like so:
S T S S T S S T S
My attempt:
$6times3times5times4times2times3times2times1times1$ which equals $4320$.
combinatorics
asked Nov 26 '18 at 18:40
Ludwigthestud
908
A class consists of three teachers (Mr. P, Ms. Q, Ms. R) and six students (Ali, Bob, Cal, Dee, Amy, Fay). How many ways can they sit in a line of 9 chairs if we have the property that between any two teachers there are exactly two students?
The correct answer is supposed to be 12,960 ways, but I cannot determine this answer. My main assumption is that there are three teachers, the two of these students will have to sit alone on the sides of the teachers. Like so:
S T S S T S S T S
My attempt:
$6times3times5times4times2times3times2times1times1$ which equals $4320$.
combinatorics
combinatorics
asked Nov 26 '18 at 18:40
Ludwigthestud
908
asked Nov 26 '18 at 18:40
Ludwigthestud
908
asked Nov 26 '18 at 18:40
Ludwigthestud
908
asked Nov 26 '18 at 18:40
Ludwigthestud
908
asked Nov 26 '18 at 18:40
Ludwigthestud
908
908
2
You can also have SSTSSTSST or TSSTSSTSS.
– JMoravitz
Nov 26 '18 at 18:41
Well, I'll be damned. My mind locked me into thinking that every two students needed a teacher to the left and right of them, but it was okay if there was lone students. I made the question harder than it needed to be.
– Ludwigthestud
Nov 26 '18 at 18:45
2
@Ludwigthestud: that gives you exactly the missing factor $3$
– Ross Millikan
Nov 26 '18 at 18:51
add a comment |
2
You can also have SSTSSTSST or TSSTSSTSS.
– JMoravitz
Nov 26 '18 at 18:41
Well, I'll be damned. My mind locked me into thinking that every two students needed a teacher to the left and right of them, but it was okay if there was lone students. I made the question harder than it needed to be.
– Ludwigthestud
Nov 26 '18 at 18:45
2
@Ludwigthestud: that gives you exactly the missing factor $3$
– Ross Millikan
Nov 26 '18 at 18:51
2
2
You can also have SSTSSTSST or TSSTSSTSS.
– JMoravitz
Nov 26 '18 at 18:41
You can also have SSTSSTSST or TSSTSSTSS.
– JMoravitz
Nov 26 '18 at 18:41
Well, I'll be damned. My mind locked me into thinking that every two students needed a teacher to the left and right of them, but it was okay if there was lone students. I made the question harder than it needed to be.
– Ludwigthestud
Nov 26 '18 at 18:45
Well, I'll be damned. My mind locked me into thinking that every two students needed a teacher to the left and right of them, but it was okay if there was lone students. I made the question harder than it needed to be.
– Ludwigthestud
Nov 26 '18 at 18:45
2
2
@Ludwigthestud: that gives you exactly the missing factor $3$
– Ross Millikan
Nov 26 '18 at 18:51
@Ludwigthestud: that gives you exactly the missing factor $3$
– Ross Millikan
Nov 26 '18 at 18:51
add a comment |
0
active
oldest
votes
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%2f3014743%2fteachers-and-students-sitting-in-a-line-with-a-condition%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3014743%2fteachers-and-students-sitting-in-a-line-with-a-condition%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
2
You can also have SSTSSTSST or TSSTSSTSS.
– JMoravitz
Nov 26 '18 at 18:41
Well, I'll be damned. My mind locked me into thinking that every two students needed a teacher to the left and right of them, but it was okay if there was lone students. I made the question harder than it needed to be.
– Ludwigthestud
Nov 26 '18 at 18:45
2
@Ludwigthestud: that gives you exactly the missing factor $3$
– Ross Millikan
Nov 26 '18 at 18:51