Page 113 - Probability Demystified

102 CHAPTER 6 The Counting Rules

PRACTICE

1. How many different batting orders can a manager make with his
starting team of 9 players?
2. In how many ways can a nurse select three patients from 8 patients to
visit in the next hour? The order of visitation is important.
3. In how many different ways can a president, vice-president, secretary,
and a treasurer be selected from a club with 15 members?
4. In how many different ways can an automobile repair shop
owner select five automobiles to be repaired if there are 8 automobiles
needing service? The order is important.
5. How many different signals using 6 flags can be made if 3 are red, 2 are
blue, and 1 is white?

ANSWERS

1. 9! ¼ 9 8 7 6 5 4 3 2 1 ¼ 362,880

8! 8! 8 7 6 5!
2. 8 P ¼ ¼ ¼ ¼ 336
3
ð 8 3Þ! 5! 5!
15! 15! 15 14 13 12 11!
3. 15 P ¼ ¼ ¼ ¼ 32,760
4
ð15 4Þ! 11! 11!
8! 8! 8 7 6 5 4 3!
4. 8 P ¼ ¼ ¼ ¼ 6720
5
ð8 5Þ! 3! 3!
6! 6 5 4 3!
5. ¼ ¼ 60
3!2!1! 3! 2 1 1

Combinations

Sometimes when selecting objects, the order in which the objects are selected
is not important. For example, when five cards are dealt in a poker game, the
order in which you receive the cards is not important. When 5 balls are
selected in a lottery, the order in which they are selected is not important.
These situations differ from permutations in which order is important and are
called combinations. A combination is a selection of objects without regard to
the order in which they are selected.