'n choose k' in Binomial Theorem
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Questions and Answers

What does 'n choose k' represent in the binomial theorem formula?

  • The exponent for the term in the binomial expansion
  • The sum of the binomial coefficients for a given n
  • The factorial of n divided by the factorial of k
  • The number of ways to choose k elements from a set of n elements (correct)
  • What is the formula for the binomial theorem?

  • (a + b)^n = Σ(n choose k) * a^k * b^(n-k), where k ranges from 0 to n
  • (a + b)^n = Σ(n choose k) * a^(n-k) * b^k, where k ranges from 0 to n (correct)
  • (a - b)^n = Σ(n choose k) * a^k * (-b)^(n-k), where k ranges from 0 to n
  • (a - b)^n = Σ(n choose k) * a^(n-k) * (-b)^k, where k ranges from 0 to n
  • What is the relationship between the binomial theorem and Pascal's triangle?

  • The terms in the binomial expansion are arranged in a pattern similar to Pascal's triangle
  • Pascal's triangle provides an alternative method for expanding binomial expressions
  • The coefficients in the binomial expansion can be found in Pascal's triangle (correct)
  • Pascal's triangle can be used to calculate the value of 'n choose k'
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