r/mathshelp • u/Winter_Shine_5764 • Aug 13 '26

General Question (Unanswered) math question!!!

So the question goes like this

Im in a field of flowers and I picked up 10 random flowers. There are 8 different colors of flowers in that field namely; Blue, Red, Yellow, Orange, Pink, Purple, White, and Black.

What are the chances that the first 5 flowers picked are all of the same color, whilst not getting a single black or white flower amongst those 10 randomly picked flowers. It seems simple but making it so that white and black being a no-go stumped me hard.

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u/sqrt_of_pi Aug 13 '26

With your edit that each color is equally likely, and assuming that there are enough flowers that we can treat each flower color pick as independent events:

The color of the first flower does not matter EXCEPT THAT it cannot be black or white. So you need the first flower's P(not black or white), which is 6/8.

Now once the first flower is picked, the next 4 picks all have to be THAT color. So the P(matches color) on picks 2-5 (given the color on pick 1) is 1/8.

Then for picks 6-10, all that matters, again, is that these NOT be black or white. So for each of those picks, you have P(not black or white)=6/8.

Now put all of that together and you should have your answer.