Combinatorics Quiz

Gloria and Bob and five other people walk through a doorway one at a time. In how many ways can the seven people go through the doorway if Bob goes through the doorway after Gloria?

• 2520

• 5040

• 1440

• 120

A child arranges 5 blocks in a row. Two blocks are painted blue, one is painted red, one is painted green and one is painted white. How many possible patterns of colours are there if the two blue blocks are next to one another?

• 24

• 120

• 48

• 60

Mr. and Mrs. Brown and their four children go to the cinema. They are randomly allocated six adjacent seats in a single row. In how many different arrangements will all the children sit next to each other?

• 144

• 5040

• 120

• 121

How many arrangements can be made using all the letters of the word ISOSCELES?

• 30240

• 362 880

• 60480

• 240

Seven people are seated at a round table. How many seating arrangements are there in which two people, Jenny and Lindsay, do not sit next to one another?

• 3600

• 1440

• 5040

• 720

In a physical education class, 5 girls are standing in a row, two of whom are sisters. In how many ways can the girls be arranged so that the sisters stand next to each other?

• 48

• 120

• 24

• 60

How many different arrangements of ten books on a shelf are possible if four detective novels must be placed next to each other?

• 120 960

• 3 628 800

• 5040

• 60 480

How many 6-digit natural numbers divisible by five can be formed using the digits 0, 1, 2, 5, 7, 9?

• 216

• 720

• 360

• 432

In how many ways can we string together 3 red, 4 blue, and 5 yellow beads?

• 27 720

• 479 001 600

• 103 680

• 55 440

In the orchestra, there are five violinists in the front row. How many different ways can they be seated?

• 120

• 5

• 60

• 24