Question

17C135 and 17C137 are examples of:

Answer 1

17C135 and 17C137 are examples of combinations or binomial coefficients.

Step-by-step explanation:

The notation nCk represents the number of ways to choose k elements from a set of n distinct elements, and it is commonly referred to as a combination or binomial coefficient. In this context, 17C135 and 17C137 indicate the number of ways to choose 135 and 137 elements, respectively, from a set of 17 distinct elements.

Combinations are used in combinatorics to count the number of ways to form subsets from a larger set without considering the order of the elements. The formula for combinations is given by
`\(nCk = (n!)/(k!(n-k)!)\)`, where n! denotes the factorial of n, which is the product of all positive integers up to n.

Answer 2

The given examples, 17C135 and 17C137, represent combinations. Combinations calculate the number of ways to choose a specific number of elements from a larger set. The formula for calculating combinations is nCk = n! / (k!(n-k)!).

Step-by-step explanation:

The given examples, 17C135 and 17C137, are representations of combinations. They are written in the form of 17C135 = 17! / (135!(17-135)!) and 17C137 = 17! / (137!(17-137)!), where the exclamation mark denotes the factorial.

Combinations are mathematical calculations that determine the number of ways to choose a specific number of elements from a larger set, disregarding the order of the elements. In this case, these combinations represent the number of ways to choose 135 and 137 elements, respectively, from a set of 17 elements.

The formula for calculating combinations: nCk = n! / (k!(n-k)!)