How to address this question?
First, we need to see that we are asked: “in how many ways a set can be selected”.
As per the definition of a set, we should know that the elements in a set don’t have an order. In other words, a set is an unordered collection of elements.
So, the set {a,b} is the same as the set {b,a}.
With this information, you should realize that we need to use combinations (and not permutations).
So, the English alphabet has 26 letters, and we should answer how many 5-combinations can be selected from a set of 26 elements.
C(26,5) =
= 26!/5!(26-5)!
=26*25*24*23*22*21!/5!21!
=7893600/120
=65780
Answer:
We can select a set of five letters from the English alphabet in 65780 ways.
Related exercises:
- List all the permutations of {a, b, c}.
- A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17 are true. If the questions can be positioned in any order, how many different answer keys are possible?
- Let S = {1,2,3,4,5}. List all the 3-permutations of S. List all the 3-combinations of S.
- How many different permutations are there of the set {a,b,c,d,e,f,g}?
- How many permutations of the letters ABCDEFG contain
- How many bit strings of length 10 contain
- How many possibilities are there for the win, place, and show (first, second, and third) positions in a horse race with 12 horses if all orders of finish are possible?
