This is another simple exercise. To solve it, we just need to apply the formula to calculate the number of 3-permutations.
“If n and r are integers with 0 ≤ r ≤ n, then P(n,r) = n! / (n−r)! ”. Discrete mathematics and its applications by Rosen.
Answer:
We just need to calculate the number of 5-permutations of 9 elements.
P(9,5) = 9!/(9-5)!
=9x8x7x6x5x4!/4!
=9x8x7x6x5
=15 120
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 value of each of these quantities
- How many permutations of {a, b, c, d, e, f, g} end with a?
