Combinatorics

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?

Tags

CCSS.HSS.CP.B.9

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?

Tags

CCSS.HSS.CP.B.9

Mr and Mrs Brown and their four children go to the cinema. They are randomly allocated six adjacent seats in a single row. What is the probability that the four children are allocated seats next to each other?

Tags

CCSS.HSS.CP.B.9

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

Tags

CCSS.HSS.CP.B.9

Seven people are seated at a round table. What is the probability that two people, Jenny and Lindsay, do not sit next to one another?

Tags

CCSS.HSS.CP.B.9

Three cards are selected at random from a standard pack of 52 cards.

What is the probability that at least two of them are clubs?

Tags

CCSS.HSS.CP.B.9

The staff in an office consists of 4 females and 7 males.

What is the probability that a randomly chosen committee of 5 staff will contain exactly 3 males?

Tags

CCSS.HSS.CP.B.9

Tags

CCSS.HSS.MD.B.7

CCSS.HSS.MD.B.6

A fair, six-sided die is thrown seven times. What is the probability, correct to three decimal places, that a ‘3’ occurs on exactly two of the seven throws?

Tags

CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

A pair of fair dice is tossed eight times. What is the probability, correct to three decimal places, of getting a sum of 9 on at least two occasions?

Tags

CCSS.HSS.CP.A.1

CCSS.HSS.CP.B.9