F

5 different flowers

6 Answers
There are 5 different flowers. kids are suppose to pick them and put them into vases. each vase has to have 3 different flowers. how many combonations are there?
C

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).

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A

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

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P

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

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E

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.

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T

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.

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K

This is actually easier than it looks - 15 different combinations.

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