# Factorials, combinations and permutations

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Calculating factorials, combinations, permutations.

Evaluate the given expressions and express all results using the usual format for writing

numbers (instead of scientific notation).

Factorial Find the number of different ways that the nine players on a baseball team can

line up for the National Anthem by evaluating 9!.

Card Playing Find the number of different possible five-card poker hands by evaluating

52 C 5.

Scheduling Routes A political strategist must visit state capitols, but she has time to

visit only 3 of them. Find the number of different possible routes by evaluating 50 P3.

Trifecta Refer to Exercise 3. Find the number of different possible trifecta bets in a race

with ten horses by evaluating 10 P3.

In Exercise 22, use the data in the accompanying table, which summarizes

challenges by tennis players (based on data reported in USA Today). The

results are from the first U.S. Open that used the Hawk-Eye electronic system

for displaying an instant replay used to determine whether the ball is in

bounds or out of bounds. In each case, assume that one of the challenges is

randomly selected.

Was the challenge to

The call successful?

Yes no

Men 201 288

Women 126 224

Tennis Instant Replay If M denotes the event of selecting a challenge made by a man,

find p (M).

In Exercise 28, refer to the following table summarizing results from a study

of people who refused to answer survey questions (based on data from "I Hear

You Knocking but You Can't Come In," by Fitzgerald and Fuller, Sociological

Methods and Research, Vol. 11, No. 1). In each case, assume that one of the subjects

is randomly selected.

AGE

18-21 22-29 30-39 40-49 50-59 60+

Responded 73 255 245 136 138 202

Refused 11 20 33 16 27 49

Survey Refusals A pharmaceutical company is interested in opinions of the elderly, because

they are either receiving Medicare or will receive it soon. What is the probability that

the selected subject is someone 60 and over who responded?

express the indicated degree of likelihood as a probability

value between 0 and 1.

Weather A WeatherBug forecast for the author's home was stated as: "Chance of rain: 80%."

Births When a baby is born, there is approximately a 50-50 chance that the baby is a girl.

Roulette When playing roulette in the Mirage Casino, you have 18 chances out of 38 of

winning if you bet that the outcome is an odd number.

Identifying Probability Values

a. What is the probability of an event that is certain to occur?

b. What is the probability of an impossible event?

c. A sample space consists of 10 separate events that are equally likely. What is the probability

Of each?

d. On a true/false test, what is the probability of answering a question correctly if you make a random guess?

e. On multiply-choice test with five possible answers for each, what is the probability of answering a question correctly If you make random guess?

Genotypes In Example 4 we noted that a study involved equally likely genotypes represented

as AA, Aa, aA, and aa. If one of these genotypes is randomly selected as in Example 4,

what is the probability that the outcome is AA? Is obtaining AA unusual?

Example 4: Genotypes When studying the affect of heredity on height,

we can express each individual genotype, AA, Aa, aA, and aa, on an index card and

shuffle the four cards and randomly select one of them. What is the probability

that we select a genotype in which the two components are different?

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##### Solution Summary

Factorials, combinations and permutations are examined in genotypes.

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Calculating factorials, combinations, permutations.

Evaluate the given expressions and express all results using the usual format for writing

numbers (instead of scientific notation).

Factorial Find the number of different ways that the nine players on a baseball team can

line up for the National Anthem by evaluating 9!. 9x8x7x6x5x4x3x2x1=362,880

Card Playing Find the number of different possible five-card poker hands by evaluating

52 C 5.52!/5!47!=2,598,960

Scheduling Routes A political strategist must visit state capitols, but she has time to

visit only 3 of them. Find the number of different possible routes by evaluating 50 P3.

50!/47!=117,600

Trifecta Refer to Exercise 3. Find the number of different possible trifecta bets in a race

with ten horses by evaluating 10 P3.

10!/7!=720

In Exercise 22, use the data in the accompanying table, which summarizes

challenges by tennis players (based on data reported in USA ...

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