- In how many ways can 3 science fiction books, 4 math books and 1 cooking book arranged on abookshelf, if
- there are no restrictions on the arrangement?
- all the science fiction books have to be stored together and also all the math books have to bestored together?
- (only) the math books have to be stored together, the rest can be arranged without restriction?
- Mike has nine friends and wants to throw a party. As his appartment is not big enough to invite all ofthem, he decides to invite only six.
- How many choices of invitations has he?
- Two of his friends of his are feuding and will not attend the party together. Accounting for thisfact, how many possibilities has he?
- Two of his friends are very close and will attend the party only if invited together. Accountingfor this fact, how many possibilities has he?
- A coin is tossed repeatedly until the first time ”heads” appears.
- Describe mathematically the sample space of this experiment.
- Describe mathematically the events
- = ”there are no more than four tails”
- = ”there are at least two tails”
- Describe mathematically the events E ∩ F and E ∪ Fc
- Given a family of events E1,E2,…,En,… on some sample space Ω, construct a new family F1,F2,…,Fn,… on the same sample space Ω such that the events Fi are monotone, (Fm ⊆ Fn for m ≤ n)and
n n [ [
Fk = for any positive integer n.
k=1 k=1
Prove that the constructed family has the desired properties.
1
