Mixing
In how many ways n seat can be placed with people from Group A and Group B and no two people from Group B...
$begingroup$
It is given that there are n seats for some event.
It is not know how many people attend from Group A or Group B.
But no two people from Group B should not sit together.
Like if there is 2 seats in event.
Valid combinations:
AA
AB
BA
Invalid combinations:
BB
What will be the number of valid combinations?
combinatorics combinations
asked Jan 26 at 15:39
Kawin MKawin M
1012
$endgroup$
add a comment |
$begingroup$
It is given that there are n seats for some event.
It is not know how many people attend from Group A or Group B.
But no two people from Group B should not sit together.
Like if there is 2 seats in event.
Valid combinations:
AA
AB
BA
Invalid combinations:
BB
What will be the number of valid combinations?
combinatorics combinations
asked Jan 26 at 15:39
Kawin MKawin M
1012
$endgroup$
add a comment |
$begingroup$
It is given that there are n seats for some event.
It is not know how many people attend from Group A or Group B.
But no two people from Group B should not sit together.
Like if there is 2 seats in event.
Valid combinations:
AA
AB
BA
Invalid combinations:
BB
What will be the number of valid combinations?
combinatorics combinations
asked Jan 26 at 15:39
Kawin MKawin M
1012
$endgroup$
It is given that there are n seats for some event.
It is not know how many people attend from Group A or Group B.
But no two people from Group B should not sit together.
Like if there is 2 seats in event.
Valid combinations:
AA
AB
BA
Invalid combinations:
BB
What will be the number of valid combinations?
combinatorics combinations
combinatorics combinations
asked Jan 26 at 15:39
Kawin MKawin M
1012
asked Jan 26 at 15:39
Kawin MKawin M
1012
asked Jan 26 at 15:39
Kawin MKawin M
1012
asked Jan 26 at 15:39
Kawin MKawin M
1012
asked Jan 26 at 15:39
Kawin MKawin M
1012
1012
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Denote the number of valid combinations by $a_n$. The first (i.e., leftmost) of the $ngeq3$ seats can be an A-seat or a B-seat. If it is an A-seat the remaining $n-1$ seats can be filled in an arbitrary admissible way. If the first seat is a B-seat the next seat has to be an A-seat, and the remaining $n-2$ seats can again be filled in an arbitrary admissible way. This leads to a recursive formula of the form
$$a_n=ldotsquad,$$
whereby the RHS has to be filled with the appropriate terms. In addition think about $a_1$ and $a_2$, and you will arrive at a familiar sequence $ldots$
answered Jan 26 at 16:18
Christian BlatterChristian Blatter
175k8115327
$endgroup$
add a comment |
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1 Answer
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active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Denote the number of valid combinations by $a_n$. The first (i.e., leftmost) of the $ngeq3$ seats can be an A-seat or a B-seat. If it is an A-seat the remaining $n-1$ seats can be filled in an arbitrary admissible way. If the first seat is a B-seat the next seat has to be an A-seat, and the remaining $n-2$ seats can again be filled in an arbitrary admissible way. This leads to a recursive formula of the form
$$a_n=ldotsquad,$$
whereby the RHS has to be filled with the appropriate terms. In addition think about $a_1$ and $a_2$, and you will arrive at a familiar sequence $ldots$
answered Jan 26 at 16:18
Christian BlatterChristian Blatter
175k8115327
$endgroup$
add a comment |
$begingroup$
Denote the number of valid combinations by $a_n$. The first (i.e., leftmost) of the $ngeq3$ seats can be an A-seat or a B-seat. If it is an A-seat the remaining $n-1$ seats can be filled in an arbitrary admissible way. If the first seat is a B-seat the next seat has to be an A-seat, and the remaining $n-2$ seats can again be filled in an arbitrary admissible way. This leads to a recursive formula of the form
$$a_n=ldotsquad,$$
whereby the RHS has to be filled with the appropriate terms. In addition think about $a_1$ and $a_2$, and you will arrive at a familiar sequence $ldots$
answered Jan 26 at 16:18
Christian BlatterChristian Blatter
175k8115327
$endgroup$
add a comment |
$begingroup$
Denote the number of valid combinations by $a_n$. The first (i.e., leftmost) of the $ngeq3$ seats can be an A-seat or a B-seat. If it is an A-seat the remaining $n-1$ seats can be filled in an arbitrary admissible way. If the first seat is a B-seat the next seat has to be an A-seat, and the remaining $n-2$ seats can again be filled in an arbitrary admissible way. This leads to a recursive formula of the form
$$a_n=ldotsquad,$$
whereby the RHS has to be filled with the appropriate terms. In addition think about $a_1$ and $a_2$, and you will arrive at a familiar sequence $ldots$
answered Jan 26 at 16:18
Christian BlatterChristian Blatter
175k8115327
$endgroup$
Denote the number of valid combinations by $a_n$. The first (i.e., leftmost) of the $ngeq3$ seats can be an A-seat or a B-seat. If it is an A-seat the remaining $n-1$ seats can be filled in an arbitrary admissible way. If the first seat is a B-seat the next seat has to be an A-seat, and the remaining $n-2$ seats can again be filled in an arbitrary admissible way. This leads to a recursive formula of the form
$$a_n=ldotsquad,$$
whereby the RHS has to be filled with the appropriate terms. In addition think about $a_1$ and $a_2$, and you will arrive at a familiar sequence $ldots$
answered Jan 26 at 16:18
Christian BlatterChristian Blatter
175k8115327
answered Jan 26 at 16:18
Christian BlatterChristian Blatter
175k8115327
answered Jan 26 at 16:18
Christian BlatterChristian Blatter
175k8115327
answered Jan 26 at 16:18
Christian BlatterChristian Blatter
175k8115327
175k8115327
add a comment |
add a comment |
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