4.1 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 ! ( 5 2 ) ! = 5 ! 3 ! = 5 × 4 × 3 ! 3 ! = 5 × 4 = 20 (b) 7 P 3 = 7 ! ( 7 3 ) ! = 7 ! 4 ! = 7 × 6 × 5 × 4 ! 4 ! = 7 × 6 × 5 = 210 (c) 9 P 4 = 9 ! ( 9 4 ) ! = 9 ! 5 ! = 9 × 8 × 7 × 6 × 5 ! 5 ! = 9 × 8 × 7 × 6 = 3024

Calculator Computation: 




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