IMO Combinatorics and Counting 2

Question 1

What is C(6, 2)?

Accepted Answer

15

Answer

C(6,2) = 6!/(2! × 4!) = (6 × 5)/(2 × 1) = 15.

Question 2

A die is rolled once. What is the probability of getting an even number?

Accepted Answer

1/2

Answer

Even numbers on a die: 2, 4, 6 — that's 3 out of 6; probability = 3/6 = 1/2.

Question 3

How many 4-letter codes can be made from 26 letters if repetition is allowed?

Accepted Answer

26⁴

Answer

With repetition allowed, each of the 4 positions has 26 choices: total = 26⁴ = 456,976.

Question 4

In how many ways can 4 people be seated in a row of 4 chairs?

Accepted Answer

24

Answer

This is 4! = 4 × 3 × 2 × 1 = 24.

Question 5

A bag has 5 red and 3 blue balls. What is the probability of picking a blue ball?

Accepted Answer

3/8

Answer

Total balls = 8; P(blue) = 3/8.

IMO - International Mathematics Olympiad Practice Test