Probability 6 Donuts 3 flavors

VVVVVV | |

VVVVV | C |

VVVVV | | S

VVVV | CC |

VVVV | C | S

VVVV | | SS

VVV | CCC |

VVV | CC | S

VVV | C | SS

VVV | | SSS

VV | CCCC |

VV | CCC | S

VV | CC | SS

VV | C | SSS

VV | | SSSS

V | CCCCC |

V | CCCC | S

V | CCC | SS

V | CC | SSS

V | C | SSSS

V | | SSSSS

| CCCCCC |

| CCCCC | S

| CCCC | SS

| CCC | SSS

| CC | SSSS

| C | SSSSS

| | SSSSSS

Probability 6 Donuts flavors by position

VVVVVV | | DDDDDD..| |

VVVVV | C | DDDDD | D |

VVVVV | | S DDDDD | | D

VVVV | CC | DDDD | DD |

VVVV | C | S DDDD | D | S

VVVV | | SS DDDD | | SS

VVV | CCC | DDD | DDD |

VVV | CC | S DDD | DD | S

VVV | C | SS DDD | D | SS

VVV | | SSS DDD | | SSS

VV | CCCC | DD | DDDD |

VV | CCC | S DD | DDD | D

VV | CC | SS DD | DD | DD

VV | C | SSS DD | D | DDD

VV | | SSSS DD | | DDDD

V | CCCCC | D | DDDDD |

V | CCCC | S D | DDDD | D

V | CCC | SS D | DDD | DD

V | CC | SSS D | DD | DDD

V | C | SSSS D | D | DDDD

V | | SSSSS D | | DDDDD

| CCCCCC | | DDDDDD |

| CCCCC | S | DDDDD | D

| CCCC | SS | DDDD | DD

| CCC | SSS | DDD | DDD

| CC | SSSS | DD | DDDD

| C | SSSSS | D | DDDDD

| | SSSSSS | | DDDDDD

Probability 6 Donuts, flavors by position, locate spacers

VVVVVV | | DDDDDD..| | 7&8

VVVVV | C | DDDDD | D | 6&8

VVVVV | | S DDDDD | | D 6&7

VVVV | CC | DDDD | DD | 5&8

VVVV | C | S DDDD | D | S 5&7

VVVV | | SS DDDD | | SS 5&6

VVV | CCC | DDD | DDD | 4&8

VVV | CC | S DDD | DD | S 4&7

VVV | C | SS DDD | D | SS 4&6

VVV | | SSS DDD | | SSS 4&5

VV | CCCC | DD | DDDD | 3&8

VV | CCC | S DD | DDD | D 3&7

VV | CC | SS DD | DD | DD 3&6

VV | C | SSS DD | D | DDD 3&5

VV | | SSSS DD | | DDDD 3&4

V | CCCCC | D | DDDDD | 2&8

V | CCCC | S D | DDDD | D 2&7

V | CCC | SS D | DDD | DD 2&6

V | CC | SSS D | DD | DDD 2&5

V | C | SSSS D | D | DDDD 2&4

V | | SSSSS D | | DDDDD 2&3

| CCCCCC | | DDDDDD | 1&8

| CCCCC | S | DDDDD | D 1&7

| CCCC | SS | DDDD | DD 1&6

| CCC | SSS | DDD | DDD 1&5

| CC | SSSS | DD | DDDD 1&4

| C | SSSSS | D | DDDDD 1&3

| | SSSSSS | | DDDDDD 1&2

Note that all unordered choices of 2 places from {1,2,3,4,5,6,7,8} are used to get the ₈C₂ or 28 choices.

There are 8 places because of the 6 donuts plus the 2 spacers needed to separate the 3 flavors.