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Questions and Answers
What is a combination in mathematics?
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)?
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?
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?
What is the number of k-combinations when k > n?
How is the set of all k-combinations of a set S often denoted?
How is the set of all k-combinations of a set S often denoted?
What is the binomial coefficient ( n b ) also known as?
What is the binomial coefficient ( n b ) also known as?
In the binomial theorem, what are the exponents b and c required to be?
In the binomial theorem, what are the exponents b and c required to be?
Which historical mathematician mentioned the special case of the binomial theorem for exponent 2?
Which historical mathematician mentioned the special case of the binomial theorem for exponent 2?
What did Indian mathematician Aryabhata's method for finding cube roots suggest he knew?
What did Indian mathematician Aryabhata's method for finding cube roots suggest he knew?
What do the coefficients ( n b ) represent in combinatorics?
What do the coefficients ( n b ) represent in combinatorics?
What does the binomial theorem describe?
What does the binomial theorem describe?
What do the exponents b and c in the binomial expansion satisfy?
What do the exponents b and c in the binomial expansion satisfy?
What is the coefficient a in the term axbyc called?
What is the coefficient a in the term axbyc called?
What were the special cases of the binomial theorem known as early as the 4th century BC?
What were the special cases of the binomial theorem known as early as the 4th century BC?
What did Indian mathematician Aryabhata's method for finding cube roots suggest he knew?
What did Indian mathematician Aryabhata's method for finding cube roots suggest he knew?
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