PERMUTATION
Permutation
Arrangement of items in a particular order
n!
Formula: nPr = P (n, r) =
n−r
Formula (circular pattern e.g., table): P = (n-1)!
Example:
1. In how many ways can six books be arranged on a shelf?
Solution:
= 6P6 or simply 6!
= 6 * 5 * 4 * 3 * 2 *1
= 720
2. Suppose there are 9 vendo machines, but only three spaces in the display room are available for the vendo
machines. In how many different ways can the 9 machines be arranged in the three available spaces?
Solution:
= 9P3
9! 9∗8∗7∗6 !
= or
9−3 6!
362880
=
720
= 504
3. In how many ways can six persons be seated around a circular table?
Solution:
= (6-1)!
= 5!
= 120
Permutation
Arrangement of items in a particular order
n!
Formula: nPr = P (n, r) =
n−r
Formula (circular pattern e.g., table): P = (n-1)!
Example:
1. In how many ways can six books be arranged on a shelf?
Solution:
= 6P6 or simply 6!
= 6 * 5 * 4 * 3 * 2 *1
= 720
2. Suppose there are 9 vendo machines, but only three spaces in the display room are available for the vendo
machines. In how many different ways can the 9 machines be arranged in the three available spaces?
Solution:
= 9P3
9! 9∗8∗7∗6 !
= or
9−3 6!
362880
=
720
= 504
3. In how many ways can six persons be seated around a circular table?
Solution:
= (6-1)!
= 5!
= 120
