Textbook

Data Management McGraw-Hill
Chapter

Chapter 3
Section

Chapter Review on Probability with Permutation, Combination

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Solutions
19 Videos

How many ways are there to arrange four boys and three girls in a line for a photo ifthe girls must be in order of height from shortest to tallest?

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Q1

How many arrangements are there of the letters in each word?

ANAGRAM

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Q2a

How many arrangements are there of the letters in each word?

EXPRESSIONS

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Q2b

The rooms m' Kendra’s apartment have 14 walls tn' total. She has enough pam't to cover 10 of these walls m' one colour and the rest m' another colour. In how many ways could Kendra pam't her apartment?

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Q3

Determine the value for `r`

that has the greatest number of combinations.

i. `C(8, r)`

ii. `C(10, r)`

iii. `C(7, r)`

iv. `C(15, r)`

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Q4

A school choir' has 10 sopranos. eight altos. seven tenors. and five basses. How many ways are there to select

a) an octet of three sopranos. two altos. two tenors. and a bass?

b) a barbershop quartet of two tenors and two basses?

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Q5

A committee of four people is to be from a fist of 10 people.

a) In how many ways could this be done?

b) Rewrite the problem so that it requires permutations in its solution.

c) Solve the new problem.

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Q6

In how many ways could five different envelopes be distributed into three mailboxes?

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Q7

You have one each of $5. $10. $20. $30. and $100 bills in your wallet. How many different sums of money could you form by reaching into your wallet and pulling out some bill's?

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Q8

You are selecting an 8-character password using 26 letters and numbers 0 through 9. In how many ways could your password contain

a) at least two letters?

b) at least two numbers?

c) at least two letters and two numbers?

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Q9

Some entries of two rows of Pascal’s triangle are given. Determine the unknown entries.

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Q10

A circle is drawn with n points situated on its circumference.

a) Using these points as vertices, how many quadrilaterals can be formed if

i) `n=4`

?

ii) `n=5`

?

iii) `n = 6`

?

b) Identify these numbers in Pascal’s triangle. Describe their location.

c) Relate these numbers to combinations in terms of combination.

d) How many quadrilaterals can be formed if `n = 12`

?

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Q11

Determine the row in Pascal’s triangle that has a sum of

a) 512

b) 4096

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Q12

Stephen’s school is four blocks west and seven blocks south of his home. Use two methods to determine the number of routes he could take to school, travelling west or south at all times.

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Q13

Use Pascal’s triangle and combinations to expand and simplify.

` (a + b)^5`

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Q14a

Use Pascal’s triangle and combinations to expand and simplify.

`(2x+y)^4`

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Q14b

A poker hand of five cards is dealt from a standard deck.

a) What is the probability that the jack, queen, and king of hearts, but no other hearts, are in the same hand?

b) What is the probability that the hand contains five hearts?

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Q15

Five students are randomly selected from seven boys and six girls to join a ski trip. What is the probability that

a) all are girls?

b) there are more boys than girls?

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Q16

A total of 25 photos have been submitted for a photo competition, three of which were submitted by you. From the submissions, five photos will be chosen as finalists.

a) What is the probability that all of your photos will be chosen as finalists?

b) What is the probability that none of your photos will be chosen as a finalist?

c) What is the probability that at least one of your photos will be chosen as a finalist?

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Q17