Taking Ribbons From A Box In The Darkness.

[devayaani]

I apologise if this is a wrong place to ask this mathematics puzzle question.
The puzzle is this:

There are 8 red, 7 green and 5 yellow ribbons in a box. How many maximum number of ribbons can be taken out of this box in the darkness (colour of the ribbons cannot be made out while taking) with the condition that in the box at least four of one colour and 3 of another colour ribbons must remain.
The answer is given as 7.
Can someone explain to me how to solve this puzzle although I have got the answer to the puzzle?
Thanking you in advance.

[JJ109]

What I would do in a situation like this is start with the smallest yellow = 5
What is the MINIMUM number that you can take out to make this a useless pile?
Answer 3. If you remove 3 then there will be 2 yellows remaining and this does not comply with either 3 or 4 remaining
Therefore you now concentrate on the greens and red
Now go to the next lowest = green. What is the MAXIMUM that you can take out to leave at least 3 greens Answer 7 - 3 = 4
Add together 3 yellows removed & 4 greens = 7
This will leave 3 green and 8 red and complies with your criteria

Now if you take 1 more (8)you could have an instance where you take 3 yellows and 5 greens and then you would not have complied with the criteria as you only have 2 yellows, 2 greens and 8 red. Only one pile complies.

[devayaani]

Thank you jj109.
Very pleased .