Quiz about Combinatorics

Question 1

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?

Accepted Answer

$$2520$$

Answer

$$240$$

Answer

$$5040$$

Answer

$$720$$

Question 2

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?

Accepted Answer

$$24$$

Answer

$$60$$

Answer

$$120$$

Answer

$$20$$

Question 3

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?

Accepted Answer

$$\frac{1}{5}$$

Answer

$$\frac{1}{15}$$

Answer

$$\frac{2}{5}$$

Answer

$$\frac{1}{30}$$

Question 4

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

Accepted Answer

$$30\ 240$$

Answer

$$362\ 880$$

Answer

$$60\ 480$$

Answer

$$90\ 720$$

Question 5

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?

Accepted Answer

$$\frac{2}{3}$$

Answer

$$\frac{1}{3}$$

Answer

$$\frac{2}{21}$$

Answer

$$\frac{1}{30}$$

Question 6

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?

Accepted Answer

$$\frac{64}{425}$$

Answer

$$\frac{7}{425}$$

Answer

$$\frac{117}{850}$$

Answer

$$\frac{1}{68}$$

Question 7

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?

Accepted Answer

$$\frac{5}{11}$$

Answer

$$\frac{5}{66}$$

Answer

$$\frac{126}{2777}$$

Answer

$$\frac{2}{11}$$

Question 8

Whenever Jeff fires an arrow in an archery competition, his probability of hitting the target is $$\frac{2}{3}$$ .

During a competition he has 10 shots at the target.

What is the probability that Jeff hits the target exactly 9 times?

Accepted Answer

$$10 imes\frac{2^9}{3^{10}}$$

Answer

$$9 imes\frac{2^9}{3^{10}}$$

Answer

$$\frac{2^9}{3^9}$$

Answer

$$\frac{2^9}{3^{10}}$$

Question 9

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?

Accepted Answer

$$0.221$$

Answer

$$0.311$$

Answer

$$0.367$$

Answer

$$0.623$$

Question 10

A group of 37 mountain hikers were travelling into the mountain ranges when a storm suddenly broke out. All the hikers rushed into 6 caves for cover. Which of the following statements are true if all the hikers picked their cave at random? Note all caves have more than enough space to hold everyone.

Accepted Answer

There will be at least one cave with at least 7 people.

Answer

There will always be 1 cave that has no people.

Answer

There will be at most two caves with at least 8 people.

Answer

There will be at least one cave with at most 5 people.

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