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

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 polygon 7 sides.How many diagonals can be formed?

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

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

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

Order does not matter

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

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

c

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

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

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

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

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

Order matters

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

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

p

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

p

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

p

Selecting a lead and an understudy for a school play.

p

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

b

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

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

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