TUTORIAL WITH WORK SHOWN FOR THE FOLLOWING QUESTIONS

1. Classify the problem according to whether it involves a permutation or a combination.

A 3-member executive committee is to be formed from a 12-member board of directors. In how many ways can it be formed?

permutation

combination

1. Classify the problem according to whether it involves a permutation or a combination.

How many four-digit numbers can be formed by using the numerals in the set {4, 6, 7, 9} if repetition is not allowed?

permutation

combination

1. Classify the problem according to whether it involves a permutation or a combination.

In how many ways can a six-letter security password be formed from letters of the alphabet if no letter is repeated?

permutation

combination

1. How many six-letter permutations can be formed from the first nine letters of the alphabet?

2. In how many ways can an investor select three mutual funds for his investment portfolio from a recommended list of eight mutual funds?

3. Find the number of distinguishable permutations that can be formed from the letters of the word PHILIPPINES.

4. In how many ways can five people boarding a bus be seated if the bus has seven vacant seats?

5. How many different signals can be made by hoisting two yellow flags, four green flags, and two red flags on a ship's mast at the same time?

6. A group of six students studying for a bar exam has formed a study group. Each member of the group will be responsible for preparing a study outline for one of six courses. In how many different ways can the six courses be assigned to the members of the group?

7. Fourteen graduate students have applied for three available teaching assistantships. In how many ways can these assistantships be awarded among the applicants if

(a) No preference is given to any one student?

(b) One particular student must be awarded an assistantship?

(c) The group of applicants includes nine men and five women and it is stipulated that at least one woman must be awarded an assistantship?

1. JCL Computers has five vacancies in its executive trainee program. In how many ways can the company select five trainees from a group of ten female and ten male applicants if the vacancies

(a) Can be filled by any combination of men and women?

(b) Must be filled by two men and three women?

1. A list of poker hands ranked in order from the highest to the lowest is shown in the following table, along with a description and example of each hand. Use the table to answer the question.

Hand Description Example

Straight

flush5 cards in sequence

in the same suitA 2 3 4 5

Four of

a kind4 cards of the same

rank and any other

cardK K K ? K ? 2

Full

house3 of a kind and a

pair3 3 3 ? 7 7

Flush5 cards of the same

suit that are not

all in sequence5 6 9 J K

Straight5 cards in sequence

but not all of the

same suit10 J Q ? K ? A

Three

of a

kind3 cards of the

same rank and 2

unmatched cardsK K K ? 2 4

Two

pair2 cards of the same

rank and 2 cards

of any other rank

with an unmatched

cardK K 2 2 ? 4 ?

One

pair2 cards of the

same rank and 3

unmatched cardsK K 5 2 ? 4

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, how many different hands consist of the following:

Four of a kind?

1. A company car that has a seating capacity of eight is to be used by eight employees who have formed a car pool. If only three of these employees can drive, how many possible seating arrangements are there for the group?

2. In how many different ways can a panel of 12 jurors and 2 alternates be chosen from a group of 19 prospective jurors?

3. A list of poker hands ranked in order from the highest to the lowest is shown in the following table, along with a description and example of each hand. Use the table to answer the question.

Hand Description Example

Straight

flush5 cards in sequence

in the same suitA 2 3 4 5

Four of

a kind4 cards of the same

rank and any other

cardK K K ? K ? 2

Full

house3 of a kind and a

pair3 3 3 ? 7 7

Flush5 cards of the same

suit that are not

all in sequence5 6 9 J K

Straight5 cards in sequence

but not all of the

same suit10 J Q ? K ? A

Three

of a

kind3 cards of the

same rank and 2

unmatched cardsK K K ? 2 4

Two

pair2 cards of the same

rank and 2 cards

of any other rank

with an unmatched

cardK K 2 2 ? 4 ?

One

pair2 cards of the

same rank and 3

unmatched cardsK K 5 2 ? 4

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, how many different hands consist of the following:

One pair?