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Counting quiz

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  • What is a permutation in counting problems?
    A permutation is an ordered arrangement of distinct objects, where each object occurs only once and the order matters.
  • How do you calculate the number of permutations of n objects taken r at a time?
    Use the formula n!/(n-r)! where n is the total number of objects and r is the number chosen.
  • What is the fundamental counting principle as applied to permutations?
    It states that the total number of arrangements is the product of the number of choices at each step.
  • How do you adjust the permutation formula for non-distinct objects?
    Divide by the factorials of the number of identical objects to account for repeated items.
  • What is the formula for permutations with non-distinct objects?
    The formula is n! divided by the product of the factorials of each type of identical object.
  • How many ways can you arrange the letters in the word 'banana'?
    There are 60 ways, calculated as 6!/(1!3!2!) for the 6 letters with 1 'b', 3 'a's, and 2 'n's.
  • What is a combination in counting problems?
    A combination is an unordered selection of objects, where the order does not matter.
  • How do you calculate the number of combinations of n objects taken r at a time?
    Use the formula n!/(n-r)!r! where n is the total and r is the number chosen.
  • How do you distinguish between a permutation and a combination?
    If the order matters, it's a permutation; if the order does not matter, it's a combination.
  • What is the notation for permutations and combinations?
    Permutations are written as P(n, r) or nPr; combinations as C(n, r) or nCr.
  • How many ways can a teacher choose a line leader and a door holder from 25 students?
    There are 600 ways, calculated as 25P2 = 25 × 24.
  • How many different 8-digit codes can be made from 5 zeros and 3 ones?
    There are 56 codes, calculated as 8!/(5!3!).
  • How many ways can you select 2 flavors from 32 for a milkshake if order doesn't matter?
    There are 496 ways, calculated as 32C2 = 32!/(30!2!).
  • How many different teams of 4 people can be formed from a group of 9?
    There are 126 teams, calculated as 9C4 = 9!/(5!4!).
  • What is the key difference between permutations and combinations?
    Permutations consider order, while combinations do not.