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.
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 or nCk or , likewise P(n,k) is often written as or nPk or with falling factorial notation (and there is more than one kind of notation for falling factorial).