1. ## Permutation/Combination?

Hi,

My question is: How many different orchid displays in a line are possible using four orchids of different colors if exactly three orchids are used?

I tried solving out the problem but I am not sure if my logic is correct. This is what I did: 4 * 3 * 2 = 24 which would classify itself as a permutation problem.

2. Hello.

Originally Posted by delishus
Hi,

My question is: How many different orchid displays in a line are possible using four orchids of different colors if exactly three orchids are used?

I tried solving out the problem but I am not sure if my logic is correct. This is what I did: 4 * 3 * 2 = 24 which would classify itself as a permutation problem.
Yes, this is correct.

Rapha

3. ## More explanation, please

Originally Posted by Rapha
Hello.

Yes, this is correct.

Rapha

But why is the "2" needed? Where does it come from?

4. Originally Posted by taiwanstats
But why is the "2" needed? Where does it come from?
There are at least two common explanations.

1) How many ways to choose the first orchid? 4.

After fixing the first orchid, how many ways to choose the second? 3.

The third? 2.

So the answer is 4 * 3 * 2.

2) How many ways to select 3 objects from 4? C(4,3).

How many ways to permute them? 3!.

So the answer is P(4,3) = C(4,3) * 3!.

C(n,k) is also written $\,_nC_k$ or nCk or $\binom{n}{k}$, likewise P(n,k) is often written as $\,_nP_k$ or nPk or with falling factorial notation (and there is more than one kind of notation for falling factorial).