I also found the answer to be 10.

You can figure this out visually by drawing five different flowers (or symbols) and connecting them together in as many ways as possible.

If you use letters instead of pictures, you can make each letter stand for a different flower: a b c d e

abc

abd

abe

acd

ace

ade

bcd

bce

bde

cde

Of course this answer is only correct if you must have three and only three flowers in each vase and each flower can only be used once (i.e. three different flowers).

If we assume that the order in which the flowers are added to the vases makes no difference, and if we assume that the flowers are called A,B,C,D,E (one letter for each of the different flowers), then the answer is 10.

Here is the set of possible flowers in the vases: ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE. This is the same number of possible collections of three flowers in 5 vases where the order is immaterial as (5x4x3)/3! = 10

The formula for combinations containing k objects selected from n possible objects is:

n ! / k ! (n-k !)

Where n ! is called n factorial and = n(n-1)(n-2)...........2 x 1

In the example there are 5 different flowers so n is 5 and the number of flowers in each vase is 3 so k is 3. Therefore the number of combinations is:

5x4x3x2x1 / (3x2x1)(2x1) = 10

So there are 10 possible combinations

Well lets see, 5 different flowers, 1,2,3,4 and 5. Arranged differently in each vase. 3 in each vase.

123

124

125

134

135

145

234

235

245

345

There are 10 ways. I also noticed that each number can be used 6 times.

God I was like at first ,wow it is difficult.But just realized it is 15 cobinations in the vase.

Very good question I really enjoyed it.