Q1. An experiment consists of rolling a 12-sided die three times. The number on top of each die is recorded. The numbers are written down in the order in which they are observed. How many possible ordered triples of numbers can result from the experiment? (Note the triple (1, 10, 3) is not the same result as the triple (3, 10, 1).)
Q2. In a lottery, when you buy a ticket, you select 7 different numbers from among the numbers 1 through 59 (order of selection does not matter), and one extra number from among the numbers 1 through 35. How many different tickets can you buy?
Q3. Consider a standard deck of cards has 52 cards and note that a poker hand consists of a sample of size 5 drawn from the deck. Answer the following questions
a) How many poker hands consist of 2 Aces and 3 Kings?
b) How many poker hands consist of 2 Aces, 2 Kings and a card of a different denomination?
c) How many Poker hands have three cards from one suit (or denomination) and two from another (a full house)?
d) A flush is a hand consisting of five cards from the same suit. How many different flushes are possible?
Q4. If you flip a coin 20 times, you will get a sequence of Heads (H) and tails (T).
a) How many different sequences of heads and tails are possible?
b) How many different sequences of heads and tails have exactly five heads?
c) How many different sequences have at most 2 heads?
d) How many different sequences have at least three heads?
Q5. Suppose an organization elects its officers from a board of trustees. If there are 30 trustees, how many possible ways could the board elect a president, vice-president, secretary, and treasurer?
Q6. Suppose you're given a list of 100 desserts and asked to rank your top 3. How many possible "top 3" lists are there?