Page 116 - Probability Demystified

CHAPTER 6 The Counting Rules 105

ANSWERS

1. n ¼ 12, r ¼ 3
12! 12! 12 11 10 9!
3
12 C ¼ ¼ ¼ ¼ 220
ð12 3Þ!3! 9!3! 9! 3 2 1
2. n ¼ 7, r ¼ 2
7! 7! 7 6 5!
C ¼ ¼ ¼ ¼ 21
7 2
ð7 2Þ!2! 5!2! 5! 2 1

3. n ¼ 15, r ¼ 10
15! 15! 15 14 13 12 11 10!
C ¼ ¼ ¼ ¼ 3003
15 10
ð15 10Þ!10! 5!10! 5 4 3 2 1 10!

4. n ¼ 8, r ¼ 3
8! 8! 8 7 6 5!
C ¼ ¼ ¼ ¼ 56 ways
8 3
ð8 3Þ!3! 5!3! 5! 3 2 1
5. If the defective calculator is included, then you must select the other

calculators from the remaining 9 calculators; hence, there are 9 C 3
ways to select the 4 calculators including the defective calculator.
9! 9! 9 8 7 6!
9 C ¼ ¼ ¼ ¼ 84 ways
3
ð9 3Þ!3! 6!3! 6! 3 2 1

Probability and the Counting Rules

A wide variety of probability problems can be solved using the counting rules
and the probability rule.
EXAMPLE: Find the probability of getting a flush (including a straight
flush) when 5 cards are dealt from a deck of 52 cards.

SOLUTION:

A flush consists of 5 cards of the same suit. That is, either 5 clubs or
5 spades or 5 hearts or 5 diamonds, and includes straight flushes.