Combinations

[pka]

Also why do i get 60 with the same method? Please help

Did you look at the link and try to answer your own question!
Study this: [imath]\displaystyle\sum\limits_{k = 3}^5 {\dbinom{5}{k}\cdot\dbinom{4}{5-k}}=81 [/imath] see if you can explain the sum to yourself!

@Cubist, The only way the given answer makes any sense is if all flowers ARE distinguishable.
Otherwise the answer is just three.

 

[Cubist]

@Cubist, The only way the given answer makes any sense is if all flowers ARE distinguishable.

That's the point I was making. You've just re-written it in a different way. The question doesn't state all flowers ARE distinguishable, but this is the only way that the answer 81 makes sense. We have to work out the question from the answer. And it doesn't seem to me like the answer was given as part of the question.

Otherwise the answer is just three.

Not so. Please see post#14 for another very valid interpretation of the question as given.


The white flowers could be distinguishable or indistinguishable
The red flowers could (separately to the white) be distinguishable or indistinguishable
Are there exactly three white flowers, or is it three or more
The ordering of the flowers in the arrangement could matter, or perhaps not

There are other assumptions that could be made too. The question ought to specify these things IMO.

 

[Harry_the_cat]

So you have 9 flowers
The flower arrangement needs to be made out of 5
Out of those 5, 3 have to be white

Where, in the question you have given us, does it say that the arrangement has to have 5 flowers?