Counting and Equations
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Questions and Answers

Which one of the following statements is true about the ordered triplets (a, b, c) that satisfy the equation $a + b + c = 10$?

  • There are infinitely many ordered triplets.
  • There is only one ordered triplet.
  • There are exactly three ordered triplets. (correct)
  • There are no ordered triplets.
  • How many ordered triplets (a, b, c) satisfy the equation $a + b + c = 10$?

  • 20
  • 10
  • 45
  • 66 (correct)
  • If a, b, and c are positive integers, what is the maximum value of a if the ordered triplet (a, b, c) satisfies the equation $a + b + c = 10$?

  • 6
  • 5 (correct)
  • 3
  • 4
  • Which one of the following statements is true about combinations?

    <p>Combinations have distinct members</p> Signup and view all the answers

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

    <p>$C(n, k) = n! / (k!(n-k)!)$</p> Signup and view all the answers

    Which of the following is true about the number of k-combinations when k is greater than n?

    <p>The number of k-combinations is zero</p> Signup and view all the answers

    If a set has 10 elements, how many 3-combinations can be drawn from this set?

    <p>252</p> Signup and view all the answers

    If a set has 5 elements, how many 5-combinations can be drawn from this set?

    <p>1</p> Signup and view all the answers

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