Factorial and Permutations Word Problems

There are six people, including you and your enemy, in a line. In how many ways can you arrange yourselves such that you and your enemy will never be beside each other?

• 240 ways

• 720 ways

• 480 ways

• 670 ways

In how many ways can you arrange seven people to be seated in a round table?

• 5040 ways

• 720 ways

• 120 ways

• 840 ways

In how many ways can a group of 8 persons arrange themselves around a circular table if 3 of them insist on sitting beside each other?

• 4,320

• 720

• 6,720

• 336

Find the number of distinguishable permutation of the letter in a word “BASKETBALL“.

• 453, 600 ways

• 45, 360 ways

• 4,536 ways

• 453 ways

Which of the following expressions represents the permutation of 7 people seated on a circular dining table?

• 7!

• (7-1)!

• (7-1)!/2

• 7P7

What is r if 6Pr = 360?

• 3

• 2

• 4

• 5

What is the number of permutations of 5 different math books piled on a table?

• 5

• 25

• 4

• 5!

Nicole has four different skirts, three different blouses and two pairs of shoes which she can wear for a business meeting. In how many ways can Nicole dress for the meeting?

• 9

• 12

• 18

• 24

A four-digit number is formed using the digits in the set {1, 2, 3, 4, 5, 6}. How many numbers can be formed if no digit can be used more than once?

• 6! = 720

• 6⁴ = 1296

• 6.5.4.3 = 360

Aleks has 5 different math books, 3 different biology books and 4 different physics books. In how many different ways can Aleks arrange his books on a book shelf?

• 5!.3!.4!

• 12!

• 5.3.4

• 5 + 3 + 4