Combinations in Mathematics Quiz

The number of k-combinations in a set with n elements is denoted as C(n, k) or C_k^n. It is calculated using factorials as $C(n, k) = \frac{n!}{k!(n-k)!}$.

Two combinations are identical if and only if each combination has the same members, and the arrangement of the members in each set does not matter. The number of k-combinations is affected by these conditions as it is equal to the binomial coefficient, which can be written using factorials as $C(n, k) = \frac{n!}{k!(n-k)!}$ whenever $k \leq n$, and which is zero when $k > n$.

A k-combination of a set S in mathematics is a subset of k distinct elements of S. It represents a selection of k items from the set S, where the order of selection does not matter.

<p>Given three fruits (apple, orange, and pear), there are three combinations of two that can be drawn from this set: an apple and a pear, an apple and an orange, or a pear and an orange.</p> Signup and view all the answers

<p>The binomial coefficient, denoted as $C(n, k)$ or $C_k^n$, is the number of ways to choose k items from n without regard to the order. It is related to the concept of combinations in mathematics as it represents the number of k-combinations in a set with n elements.</p> Signup and view all the answers