15 Questions
What is a combination in mathematics?
A selection of items from a set where the order of selection does not matter
How many combinations of two can be drawn from a set of three fruits (apple, orange, pear)?
3
What is the formula for the number of k-combinations from a set of n elements?
$C(n,k) = \frac{n!}{k!(n-k)!}$
What is the number of k-combinations when k > n?
Zero
How is the set of all k-combinations of a set S often denoted?
$(S choose k)$
What is the binomial coefficient ( n b ) also known as?
Combinatorial coefficient
In the binomial theorem, what are the exponents b and c required to be?
Nonnegative integers
Which historical mathematician mentioned the special case of the binomial theorem for exponent 2?
Euclid
What did Indian mathematician Aryabhata's method for finding cube roots suggest he knew?
The binomial formula for exponent 3
What do the coefficients ( n b ) represent in combinatorics?
Number of combinations
What does the binomial theorem describe?
Expansion of powers of a binomial
What do the exponents b and c in the binomial expansion satisfy?
b + c = n
What is the coefficient a in the term axbyc called?
Combination coefficient
What were the special cases of the binomial theorem known as early as the 4th century BC?
Expansion for exponent 2
What did Indian mathematician Aryabhata's method for finding cube roots suggest he knew?
The binomial formula for exponent 3
Test your understanding of combinations in mathematics with this quiz. Explore the concept of selecting items from a set without considering the order of selection.
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