A box contains 10 light bulbs. Find the number of n of ordered samples of (a) size 5 with replacement, and (b) size 5 without replacement.

Given:

(a) There are 5 houses in 5 different colors.
(b) In each house lives a person with a different nationality.
(c) These 5 people drink a certain drink, smoke a certain cigar and have a particular pet.
(d) None of the people have the same pet, smoke the same cigar nor drink the same drink.

From the following statements, determine who will Keep the Fish

1: The Brit lives in a red house.
2: The Swede keeps dogs as pets.
3: The Dane drinks tea.
4: The green house is on the left of the white house.
5: The green house owner drinks coffee.
6: The person who smokes Pall Mall rears birds.
7: The owner of the yellow house smokes Dunhill.
8: The man living in the house right in the centre drinks milk.
9: The Norwegian lives in the first house.
10: The man who smokes Blend lives next to the one who keeps cats.
11: The man who keeps horses lives next to the man who smokes Dunhill.
12: The owner who smokes Blue Master drinks beer.
13: The German smokes Prince.
14: The Norwegian lives next to the blue house.
15: The man who smokes Blend has a neighbor who drinks water.

How many positive integers can be formed from the digits 1, 2, 3, and 4 if no digit is repeated in any one integer?