Page 110 - Probability Demystified

CHAPTER 6 The Counting Rules 99

SOLUTIONS

1. 2! ¼ 2 1 ¼ 2
2. 7! ¼ 7 6 5 4 3 2 1 ¼ 5040
3. 9! ¼ 9 8 7 6 5 4 3 2 1 ¼ 362,880
4. 4! ¼ 4 3 2 1 ¼ 24
5. 6! 3!¼6 5 4 3 2 1 3 2 1 ¼ 4320
6. 4! 8! ¼ 4 3 2 1 8 7 6 5 4 3 2 1 ¼ 967,680
7. 7! 2!¼7 6 5 4 3 2 1 2 1 ¼ 10,080
10! 10 9 8!
8. ¼ ¼ 10 9 ¼ 90
8! 8!
5! 5 4 3 2!
9. ¼ ¼ 5 4 3 ¼ 60
2! 2!
6! 6 5 4 3!
10. ¼ ¼ 6 5 4 ¼ 120
3! 3!

The Permutation Rules

The second way to determine the number of outcomes of an event is to use
the permutation rules. An arrangement of n distinct objects in a specific order
is called a permutation. For example, if an art dealer had 3 paintings, say A,
B, and C, to arrange in a row on a wall, there would be 6 distinct ways to
display the paintings. They are

ABC BAC CAB
ACB BCA CBA

The total number of different ways can be found using the fundamental
counting rule. There are 3 ways to select the first object, 2 ways to select the
second object, and 1 way to select the third object. Hence, there are
3 2 1 ¼ 6 different ways to arrange three objects in a row on a shelf.
Another way to solve this kind of problem is to use permutations. The
number of permutations of n objects using all the objects is n!.