# Math, possibility!!! (1 Viewer)

#### Kathy358

##### New Member
A box contains 10 red candies, 8 yellow candies and 6 blue candies. Randomly take out 4 candies from the box. What is the possibility that 4 candies are of all three colours?

#### InteGrand

##### Well-Known Member
A box contains 10 red candies, 8 yellow candies and 6 blue candies. Randomly take out 4 candies from the box. What is the possibility that 4 candies are of all three colours?
$\bg_white \noindent \textbf{Hint.} You can do it by breaking it up into cases. Find the number of ways to pick four candies so that your colours picked are (where order of picking is unimportant): (i) RRYB; (ii) RYYB; (iii) RYBB. (Those three cases are the only ways to have all three colours picked in your selection of four candies.) After finding all the ways you can do these, add them up and divide by the total number of ways to pick four candies from the box.$

#### InteGrand

##### Well-Known Member
Can you please have a look at my working to see if it's correct or not? Thank you!
https://imgur.com/a/y3ZiV
This is not correct. You are counting things as though order matters for the total number of ways to pick four candies from the 24 in the box. But when you are counting the number of ways for each of the cases (e.g. RRYB), you have counted the ordering as though the reds must come first, then the yellow, then the blue. You didn't take into account cases where yellow came first, then blue, then the reds, etc. (which are still cases where we pick two reds, one yellow, and one blue, etc.). So you have undercounted the desirable outcomes, so your answer is less than the true answer.

It is easier to do this problem by just assuming always that the order is unimportant.

Last edited:

#### Kathy358

##### New Member
sorry but i still don't understand, probably because English is not my first language. Can you please explain to me more detailedly? What do you mean "you have counted the ordering as though the reds must come first, then the yellow, then the blue. You didn't take into account cases where yellow came first, then blue, then the reds, etc. (which are still cases where we pick two reds, one yellow, and one blue, etc." Why does the way I did mean like that? What is the difference between my way and the correct way. Thanks a lot!

#### dan964

##### MOD
Moderator
The order of RRYB is unimportant, meaning that I could pick out YBRR for example. Your working does not account for these rearrangements

#### Kathy358

##### New Member
So can you please show me the right way to do? Thanks a lot!