The Principle of Inclusion and Exclusion

Question 1

In how many ways 7 balloons of different colours hanging on a wall can be arranged so that no balloon is in its original position.

Answer 1

1854

Question 2

Let |A| = 15, |B| = 12 & |A n B| = 7. Find |A u B|.

Answer 2

20

Question 3

Let |P| = 17, |Q| = 12, |R| =20, |P n Q| = 5, |Q n R| = 6, |R n P| = 7 & |P n Q n R| = 11. Find |P u Q u R|.

Answer 3

42

Question 4

How many numbers are there between 0 and 500 which are neither multiple of 5 nor 11?

Answer 4

360

Question 5

On a station, 6 passengers went to a cloakroom and deposited their luggage for 2 hours. Find the number of ways that no one gets back his luggage.

Answer 5

265