This type of exercise is easy. You are only required to apply a formula. You just need to know the formula.
“If n and r are integers with 0 ≤ r ≤ n, then P(n,r) = n! / (n−r)! ”. Discrete mathematics and its applications by Rosen.
Table of Contents
a) P(6,3)
P(6,3)=6!/(6-3)!
=6!/3!
=6x5x4x3!/3!
=120
b) P(6,5)
P(6,5)= 6!/(6-5)!
=6!/1!
=6!
=720
c) P(8,1)
P(8,1)=8!/(8-1)!
=8×7!/7!
=8
d) P(8,5)
P(8,5)=8!/(8-5)!
=8*7*6*5*4*3!/3!
= 6720
e) P(8,8)
P(8,8)=8!/(8-8)!
=8!/0!
=8!/1
= 403 020
f) P(10,9)
P(10,9)= 10!/(10-9)!
=10!/1!
=10!
= 3 628 800
As a final note, you won’t usually find this type of exercise. However, it is important to know the formula.
Here is how you will usually apply this formula.
Typical exercise: in how many ways can you choose first, second, and third place in a competition of 10 people if there are no ties? Answer: P(10,3). Notice, that the order matters because there might different arrangements for the same three people.
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
- How many permutations of {a, b, c, d, e, f, g} end with a?
