1. An icecream store sells two drinks (sodas or milk shakes) in four sizes (small, medium, large or jumbo) and five flavors (vanilla, strawberry, chocolate, coffee or pistachio). In how many ways can a customer order a drink?
2. A club with tem members is to choose three officers - president, vice-president and secretary treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?
3. Of 12 possible books, you plan to take 4 with you on vacation. How many different collections of 4 books can you take?
4. To win at LOTTO in the state of Florida, one must corectly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possiable?
6. A poker hand consists of five cards.
a) Find the total number of possible five-card poker hands.
b) A diamond flush is a five-card hand consisting of all diamonds. Find the number of possible diamond flushes.
c) Find the probability of being dealt a diamond flush.
7. The probability that South Florida will be hit by a major hurricane (category 4 or 5) in any single year is 1/16.
a) What is the probability that South Florida will be hit by a major hurricane two years in a row?
b) What is the probability that South Florida will be hit by a major hurricane in three consecutive years?
c) What is the probability that South Florida will not be hit by a major hurricane in the next ten years?
d) What is the probability that South Florida will be hit by a major hurricane at least once in the next ten years?
This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Algebra and provides students with a clear perspective of the underlying concepts.