Math30-1 »» Permutation or Combination?

A committee of 7 consisting of a chairman, vice chairman, a secretary, and 4 other members is to be chosen from a class of 20 students. In how many ways can this committee be chosen?

b

From 5 consonants and 4 vowels, how many words can be formed using 3 consonants and 2 vowels?

b

Given 7 consonants and 4 vowels, how many 5-letter arrangements can be made if each arrangement consists of 3 different consonants and 2 different vowels?

b

The number of quadrilaterals that can be formed using six distinct points on the circumference of a circle is...?

c

How many schedules can be made if 6 classes are chosen from a list of 25?

p

How many three digit numbers can you make with the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9?

p

How many ways can 3 people be seated on 5 chairs?

p

How many ways can a baseball manager arrange the batting order of nine players?

p

How many ways can you arrange 8 cars?

p

Order matters

p

You own 7 different books and are arranging them on a shelf.

p

You are selecting 2 appetizers from a restaurant menu consisting of 4 appetizers.

c

You have 4 different sweaters and you are going to bring 2 of them along with you on a trip.

c

You have 8 friends, and you will select 2 of them to go to a movie with you, since you have 2 extra tickets.

c

You just got a free ticket for a boat ride, and you can bring along 2 friends! Unfortunately, you have 5 friends who want to come along. How many different groups of friends could you take with you?

c

6 students are competing in a race; the first place, second place, and third place ribbons will be handed out to three students.

p

A photographer is arranging a family of 6 people in line for a photo.

p

Assigning students to their seats on the first day of school.

p

At the start of the year, a new teacher is making a seating plan for her class. If there are 20 students in her class, how many seating plans could she make?

p

Determine the number of grad-committee executives consisting of a President, Vice-President, Treasurer and Secretary that can be formed from a group of 15.

p

How many arrangements of the letters of the word 'BENGALI' can be made (i) If the vowels are never together. (ii) If the vowels are to occupy only odd places.

p

How many passwords can be made using the letters A, B, C, D, E, and F? (Using each letter only once)

p

If you have 6 New Year greeting cards and you want to send them to 4 of your friends, in how many ways can this be done?

p

In a club of 30 members, how many ways can a president and vice president be chosen?

p

In a ten horse race, how many ways can the horses come in first, second, and third?

p

Vanessa is packing her bags for her vacation. She has 5 unique action figures, but only 3 fit in her bag. How many different groups of 3 action figures can she take?

c

Order does not matter

c

12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?

c

A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when: (i) At least 2 women are included? (ii) At most 2 women are included?

c

A polygon 7 sides.How many diagonals can be formed?

c

There are 5 novels and 4 biographies. In how many ways can 4 novels and 2 biographies can be arranged on a shelf?

b

There are 7 men and 10 women on a committee selection pool. A committee consisting of President, Vice-President, and Treasurer is to be formed. How many ways can exactly two men be on the committee ?

b

A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

c

A question paper consists of 10 questions divided into two parts A and B. Each part contains five questions. A candidate is required to attempt six questions in all of which at least 2 should be from part A and at least 2 from part B. In how many ways can the candidate select the questions if he can answer all questions equally well?

c

A research team of 6 scientists is to be chosen from 10 chemists, 14 biologists, and 12 physicists. How many possible research teams could be formed containing at most 1 physicist.

c

A school committee of 5 is to be formed from 12 students.How many committees can be formed if John must be on the committee?

c

A student council of 5 members is to be formed from a selection pool of 6 boys and 8 girls. How many councils can have Jason on the council?

c

Barry owns 5 dogs and he is taking 3 of them out for a walk.

c

Brandon wants to take 3 dogs with him on his morning walk. If Brandon owns 8 dogs, how many different groups of dogs can he choose for his walk?

c

Determine the number of four card hands that contain at least 2 clubs.

c

Find the number of subsets of the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} having 4 elements.

c

From 8 men and 5 women, a committee of 4 is selected. How many groups will have 3 women and 1 man?

c

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

c

How many committees are possible if 5 people are chosen from 30?

c

How many ways are there to deal a five-card hand consisting of three eight's and two sevens?

c

How many ways can 3 CDs be selected from a collection of 10 CDs?

c

How many ways can two books be picked from a list of six?

c

How many ways can two cards be chosen from a deck of 52?

c

How many ways can two puppies be chosen from a litter of five?

c

If ten people shake hands with each other only once, What is the total number of handshakes?

c

In a box, there are 5 black pens, 3 white pens and 4 red pens. In how many ways can 2 black pens, 2 white pens and 2 red pens can be chosen?

c

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

c

In a group of 9 people, there are 4 females and 5 males. Determine the number of 4-member committees consisting of at least 1 female that can be formed.

c

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

c

In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

c

In how many ways can a poker player obtain a 5 card hand that contains exactly three aces?

c

Jessica is packing her bags for her vacation. She has 8 unique tigers, but only 4 fit in her bag. How many different groups of 4 tigers can she take?

c

Michael is packing his bags for his vacation. He has 6 unique socks, but only 5 fit in his bag. How many different groups of 5 socks can he take?

c

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

c

Selecting three students to attend a conference in Washington, D.C.

c

The Gamma Zeta Beta fraternity must choose a committee of four members to plan its annual Children's Hospital fund raiser and beer bash. If the fraternity has 10 members, how many different committees can be chosen?

c

The Indian Cricket team consists of 16 players. It includes 2 wicket keepers and 5 bowlers. In how many ways can a cricket eleven be selected if we have to select 1 wicket keeper and at least 4 bowlers?

c

There are 18 math students currently enrolled in Math 30-1. A committee of 4 members is to be set up to discuss the format of the review sessions for the Diploma Exam. How many ways can the committee members be selected to participate in this project?

c

In how many different ways can five persons stand in a line for a group photograph?

p

In how many ways can 4 girls and 5 boys be arranged in a row so that all the four girls are together?

p

In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together?

p

In how many ways can the letters of the word "PROBLEM" be rearranged to make 7 letter words such that none of the letters repeat?

p

Selecting a lead and an understudy for a school play.

p

Suppose 7 students are staying in a hall in a hostel and they are allotted 7 beds. Among them, Parvin does not want a bed next to Anju because Anju snores. Then, in how many ways can you allot the beds?

p

Suppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it?

p

The Gamma Zeta Beta fraternity is electing a President, Vice President, Secretary, and Kegger Chair. If the fraternity has 10 members, in how many different ways can the officers be chosen?

p

There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairy tales, novels and plays.

p

You received 5 Christmas cards and you want to arrange them on the single level shelf above your fireplace.

p