“A permutation of a set of distinct objects is an ordered arrangement of these objects.”
We can follow a simple approach to solve this exercise.
If we calculate how many permutations are there in the set {b, c, d, e, f, g} (the original set without ‘a’), we will know how many permutations of the original set end with a.
It is the same number. Notice that we can get each permutation and add ‘a’ at the end.
So, the original set has 7 elements. So, let’s calculate how many permutations are there in a set with 6 elements.
The first element can be chosen in 6 ways. For each of those 6 ways, the second element can be chosen in 5 ways, and so on.
It follows that we must apply the multiplication rule.
6x5x4x3x2x1=720.
Answer:
There are 720 permutations of {a, b, c, d, e, f, g} that ends with a.
Related exercises:
- A group contains n men and n women. How many ways are there to arrange these people in a row if the men and women alternate?
- There are six different candidates for governor of a state. In how many different orders can the names of the candidates be printed on a ballot?
- In how many different orders can five runners finish a race if no ties are allowed?
- Find the value of each of these quantities a) C(5,1) b) C(5,3) c) C(8,4) d) C(8,8) e) C(8,0) f) C(12,6)
- Find the number of 5-permutations of a set with nine elements
- Find the value of each of these quantities
