IMO Combinatorics and Counting

Question 1

In how many ways can you arrange 3 books on a shelf?

Accepted Answer

6

Answer

3

Answer

9

Answer

12

Question 2

A coin is tossed 3 times. How many possible outcomes are there?

Accepted Answer

8

Answer

4

Answer

6

Answer

10

Question 3

How many 2-digit numbers can be formed using digits 1, 2, 3, 4 (without repetition)?

Accepted Answer

12

Answer

8

Answer

10

Answer

16

Question 4

In how many ways can a committee of 2 be chosen from 5 people?

Accepted Answer

10

Answer

5

Answer

8

Answer

20

Question 5

How many ways can first, second, and third prizes be awarded to 6 contestants?

Accepted Answer

120

Answer

18

Answer

60

Answer

90

Question 6

A menu has 4 starters and 3 main courses. How many different meals (one starter + one main) are possible?

Accepted Answer

12

Answer

7

Answer

10

Answer

14