Combinations of flowers (security geek's collection)

[alex_cute]

Hi guys,

First of all, thanks for all the problems you post, that's a great place to share knowledge!

Could you please explain the way to solve the below problem.

In a flower shop, there are 5 different types of flowers. Two of the flowers are blue, two are red and one is yellow. In how many different combinations of different colors can a 3-flower garland be made?


a) 4.

b) 20.

c) 3.

d) 5.

e) 6.

My approach was:

One can make garlands of flowers using different colors in the following way:
B-R-Y
B-R-B
B-Y-B
R-R-Y
R-B-R

Others would repeat the above combinations (like R-Y-R etc.).

[penfriend]

I assume there is no repetition of flowers of same color. If that is the case, we have an arrangement problem with n things n! hence 6

[gorby13]

Hi,

I think the answer is (A) 4.

Explaination:- Repetition of colors is not allowed in the 3 flower bouquet. So we have 2 choices for RED, 2 for BLUE and 1 for Yellow,
i.e 2*2*1 = 4.

[arjmen]

Hi,

I think the answer is (A) 4.

Explaination:- Repetition of colors is not allowed in the 3 flower bouquet. So we have 2 choices for RED, 2 for BLUE and 1 for Yellow,
i.e 2*2*1 = 4.

Agreed with A.

This question involves such small numbers that it completely wipes out an important concept.

Lets see another example:

There are 20 flowers of different types. 5-Red, 4-Blue, 6-white, 2-yellow, 2-green and 1-violet. How many different 6-flower garlands can be made where every flower is of a different colour?

[alex_cute]

If you try to make bunches of flowers (as I did above) such that each has different combination of colors, you will get 5 possible ways to arrange them. Is there any mistake in my reasoning?

[arjmen]

If you try to make bunches of flowers (as I did above) such that each has different combination of colors, you will get 5 possible ways to arrange them. Is there any mistake in my reasoning?

Don't the colours have to be different?
e.g. RRY => 2 reds

[alex_cute]

I presume the answer to Arjmen's question would be 5*4*6*2*2*1 = 480. Is that correct?

However, I would like to know the reasoning for the first problem cause as far as Arjmen's example as concerned, it is quite difficult to show the exact combinations of colors (since the numbers involved are indeed large)...

[alex_cute]

Don't the colours have to be different?
e.g. RRY => 2 reds

I think that's fine because we are told we have 2 RED flowers and 2 BLUE ones.

[arjmen]

I think that's fine because we are told we have 2 RED flowers and 2 BLUE ones.

In how many different combinations of different colors can a 3-flower garland be made?

Doesn't the above imply that the garland must be made of 3 different colours? A red flower is of the same colour as another red flower.

[alex_cute]

Doesn't the above imply that the garland must be made of 3 different colours? A red flower is of the same colour as another red flower.

I understand that. However, in this case we will not be able to use ANY two same colors, i.e. 2 BLUE ones and 2 RED once in the same combination... Then if we write the colors for the garlands, they will be:
B-R-Y only?

If we use 2 colors for both BLUE and RED, then we will have:

one for diff. colors: B-R-Y
then 2 for BLUE: B-Y-B and B-R-B
then 2 for RED: R-Y-R and R-B-R

I would very much appreciate if anyone can point to the mistake here. The Official Answer is indeed 4. )