Page 120 - Probability Demystified

CHAPTER 6 The Counting Rules 109

There are 10 C 3 ways to select 3 people.

9! 9! 10! 10!
3
10 C ¼ ¼ ¼ 84 ¼ ¼ 120
ð9 3Þ!3! 6!3! ð10 3Þ!3! 7!3!
60 1
Pð2 nurses and 1 doctorÞ¼ ¼
120 2
5. There are 13 cards in each suit; hence, there are 13 ways to get 4 of a
kind and 48 ways to get the fifth card. Therefore, there are 624 ways
to get 4 of a kind. There are 52 C 5 ways to deal 5 cards.
52!
C ¼ ¼ 2,598,960
52 5
47!5!
Hence,
624 13
Pð4 of a kindÞ¼ ¼ 0:0002
2,598,960 54,145

Summary

In order to determine the number of outcomes of events, the fundamental
counting rule, the permutation rules, and the combination rule can be used.
The difference between a permutation and a combination is that for a
permutation, the order or arrangement of the objects is important. For
example, order is important in phone numbers, identification tags, social
security numbers, license plates, etc. Order is not important when selecting
objects from a group. Many probability problems can be solved by using the
counting rules to determine the number of outcomes of the events that are
used in the problems.

CHAPTER QUIZ

1. The value of 6! is
a. 6
b. 30
c. 120
d. 720