A batch code on the side of a food container is composed of seven dots, two blue, two white and three black.
if five dots chosen from the seven dots. Find the number of different possible codes in this case.

Question

A batch code on the side of a food container is composed of seven dots, two blue, two white and three black.
if five dots chosen from the seven dots. Find the number of different possible codes in this case.

anonymous · Answer

This looks like more a programming problem. Is this a programming problem?

anonymous · Answer

Ok so I have a solution:
B B W W Bk Bk Bk
Now we work with an omission pattern through the list until we have a repetition:
B .   .   W Bk Bk Bk 
B B .    .   Bk Bk Bk
B B W .    .    Bk Bk
B B W W .     .    Bk
[B B W W Bk  .    .]-->repeated
.   B W W Bk Bk .
.   .   W W Bk Bk Bk

To see if that the final we have to ensure that every possible pair of color has been ommitted at the same time:
BB:check
WW: check
BkBk: check
BW: check
BBk:check
WBk:check

So the above combinations are the only ones possible!
Notice that one line is repeated, which leaves us with 6 possible different codes. Funnily enough this is also the number of possible omission pair! (BB,WW,BkBk,BW,BBk,WBk)

This is not a coincidence.
If we were considering 4-dots codes, we'd have to count all the possible triplets. 
Hope i helped :)