6.1 Permutations Part 2

(C) Permutation of n Different Objects, Taken r at a Time

1. The number of permutations of n different objects, taken r at a time is given by :

2.  A permutation of n different objects, taken r at a time, is an arrangement of a set of r objects chosen from n objects. The order of the objects in the chosen set is taken into consideration.

3. The number of permutations of n different objects, taken all at a time, is :


Example 1:
Evaluate each of the following.
(a)  5 P 2 (b)  7 P 3 (c)  9 P 4

Solution:
(a)  5 P 2 = 5! ( 52 )! = 5! 3! = 5 ×4 ×3! 3! =5×4=20 (b)  7 P 3 = 7! ( 73 )! = 7! 4! = 7 ×6 ×5 ×4! 4! =7×6×5=210 (c)  9 P 4 = 9! ( 94 )! = 9! 5! = 9 ×8 ×7 ×6 ×5! 5! =9×8×7×6=3024


Calculator Computation: