Combinations in Mathematics Quiz
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Questions and Answers

What is a combination in mathematics?

  • A rearrangement of items within a set
  • A selection of items from a set where the order of selection does not matter (correct)
  • A subset of distinct elements where the count matters
  • A selection of items from a set where the order of selection matters

    • How many combinations of two can be drawn from a set of three fruits (apple, orange, pear)?

  • 6
  • 1
  • 2
  • 3 (correct)

    • What is the formula for the number of k-combinations from a set of n elements?

  • $C(n,k) = \frac{n}{k} \times (n - k)$
  • $C(n,k) = n^k$
  • $C(n,k) = n + k$
  • $C(n,k) = \frac{n!}{k!(n-k)!}$ (correct)

    • What is the number of k-combinations when k > n?

    <p>Zero</p> Signup and view all the answers

    How is the set of all k-combinations of a set S often denoted?

    <p>$(S choose k)$</p> Signup and view all the answers

    What is the binomial coefficient ( n b ) also known as?

    <p>Combinatorial coefficient</p> Signup and view all the answers

    In the binomial theorem, what are the exponents b and c required to be?

    <p>Nonnegative integers</p> Signup and view all the answers

    Which historical mathematician mentioned the special case of the binomial theorem for exponent 2?

    <p>Euclid</p> Signup and view all the answers

    What did Indian mathematician Aryabhata's method for finding cube roots suggest he knew?

    <p>The binomial formula for exponent 3</p> Signup and view all the answers

    What do the coefficients ( n b ) represent in combinatorics?

    <p>Number of combinations</p> Signup and view all the answers

    What does the binomial theorem describe?

    <p>Expansion of powers of a binomial</p> Signup and view all the answers

    What do the exponents b and c in the binomial expansion satisfy?

    <p>b + c = n</p> Signup and view all the answers

    What is the coefficient a in the term axbyc called?

    <p>Combination coefficient</p> Signup and view all the answers

    What were the special cases of the binomial theorem known as early as the 4th century BC?

    <p>Expansion for exponent 2</p> Signup and view all the answers

    What did Indian mathematician Aryabhata's method for finding cube roots suggest he knew?

    <p>The binomial formula for exponent 3</p> Signup and view all the answers

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