PERMUTATIONS
(involving DIFFERENT OBJECTS)
WARM-UP QUESTION
How many different arrangements of the letters of the word GOD exist?
A permutation of n distinct items is an arrangement
of ALL the items in a definite order.
PERMUTATION NOTATION (P-notation)
PERMUTATION NOTATION:
n Pr
= P(n,r)
n!
=
(n  r )!
where P(n,r) is the number of permutations
of n objects taken r at a time and 0  r  n.
For example, 8 P6
EXAMPLE #1
a)
12P8
Evaluate each of the following:
(manually)
EXAMPLE #2
a) 7 x 6 x 5
= P(8,6)
8!
=
(8  6)!
8!
=
2!
b)
15P5
(with calculator)
Express each of the following in P-notation:
b) 100 x 99 x 98 x 97 x 96
EXAMPLE #3
Determine the number of permutations that exist
using the letters of the word QUESTION if:
a) all 8 letters are used;
Slot Method:
___ ___ ___ ___ ___ ___ ___ ___
Factorial Notation:
P-notation:
b) only 3 letters are used.
Slot Method:
___ ___ ___
P-notation:
EXAMPLE #4
Using a standard deck of 52 cards, determine the
number of ways the following can be dealt:
a) 3 cards
EXAMPLE #5
b) 3 red cards
c) 2 Jacks
Six children line up for a photograph. Determine
the number of arrangements that are possible if:
a) there are NO restrictions;
b) Pebbles is in the third position and BamBam is in the sixth position;
c) the children stand in a circle;
The number of ways n objects
can be arranged in a circle
is (n–1)!
d) Pebbles and BamBam cannot stand beside each other in the circle.