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p(IM,2N) = 044” SECTlON 11.5 Probability with the Fundamental Counting Principle. Permutations, and Combinations 639 Now we can fill in the numbers in the numerator and the denominator of our
probability fraction. j; o P 1 man 2 women = . . .
( ’ ) total number of possrble combinations ,1ng one man and two women is 2%. O A club consists of six men and four women. Three members are selected at
random to attend a conference: Find the probability that the selected group consists of a. three men.
b. two men and one woman. 7 . IffEXERClSE SET 11.5 oooeeo , 3 'Practice and Application Exercises EsjA group consists of four men and five women. Three " people are selected to attend a conference. ' a. In 110w many ways can three pebple be selected from 
this group of nine? . 9C3 7 34 ' person arrives at a different time. (2’07
a. In how many ways can they arrive? gift :31 12:1: f 'b. In how many ways can three women be selected from
the five women? 5 C 3 :40 1. Martha, Lee, Nancy, Paul, and Armando have all been
invited to a dinner party. They arrive randomly and each h. ES??? 11131? wags‘crg Maﬁflﬁ‘rgf and Armando c. Find the probability that the selected ro will consist
‘ . E _.'_l «—— — A *— . . . W ofall women. (76¢) : til—$914 132422"
0 Find the probability that Martha WI“ arrive ﬁmt and l 6. Apolitical discussion group consist? of five e ocrats and iv .— 1: ,__ﬂ.
Armando last. i309”: J A Md) "‘ 6%?" 20 six Republicans. Four people are selected to attend a
. Three men and three women line up at a checkout counter *— conference. in a store. 6[ : (i229 i a. In how many ways can four people be selected from this a. In how many ways can they line up? ' group of eleven? h. In how many ways can they line up if the first person in b. In how many ways can four Republicans be selected
line is a woman, and then the line alternates by , from the six Republicans?
gender—that 15 agomt’jﬁl, a Ea“! a woman—,3 man and c. Find the probability that the selected group will consist
so on? i “(A ’ _ '___' “L L I a of all Republicans. c. Find the probability that the first person in line is a 7 To play the California lottery, a person has to correctly woman and the line alternates by gender. P( E) : 25‘” £7— select 6 out of 51 numbers, paying $1 for each six—number . h 120 ,
. Six standup comics, A, B, C, D, E, and F, are to performij , selection. If the six numbers plcked are the same as the on a single evening at a comedy club. The order of ‘ ”" ones drawn by the lottery, mountains of money are performance is determined by random selection. Find the *" bestowed. What is the probability that a person with one ‘ probability that 59mm {MPH 53' E 3: _‘_i_ .2 E J. combination of six numbers will win? What is the probabil 3. Comic B will perform first. 4 E i %:[_g: P(E)ity of winning if 100 different lottery tickets are purchased?
b, Comic c will perform ﬁfth and comic B will peIfOEQ 8. A state lottery is designed so that a player chooses five last. __. __ _ g. 9 E _ 24, PO?) f 2% # it numbers from 1 to 30 on one lottery ticket. What is the
. . _, . . " 93° babilit that a la er with one letter r ticket will win? 0. th 1 "Had : pro y p y . 5
The comedians Will perfor m e f0 lowmg or er What is the probability of winning if 100 different lottery .: i _ J.
EB, C’A’B’E Pg) 9‘40 WA) 5“}; ) W5) “ 3 tickets are purchased?
3 . @ Comic A or comic B will per o’rTrﬁirst. PMWB) 
' " A box contains 25 transistors, 6 of which are defective. If 4 Seven performers, A, B, C, D,E,F, and G, are to appear in a . . .
fund raiser. The order of performance is determined by 6 are 561%th at random, ﬁnd the probability that random selection. Find the probability that
a. D will perform first. a. all are defective.
b. none are defective. b. B will perform sixth and B will perform last. 10. A committee of five people is to be formed from six
c. They will perform in the following order: C, D, B, A, G, lawyers and seven teachers. Find the probability that
F, E. a. all are lawyers. d. F or G will perform first. in. none are lawyers. ...
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 Spring '11
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