Question

Indicate the formula for the following conditions: C(n, r) = ?

A) n! / (r! * (n-r)!)
B) n! / r!
C) r! / n!
D) n! * r!

Answer 1

The correct formula for C(n, r), which expresses the number of ways to choose r items from a set of n items, is n! / (r! * (n-r)!), indicated by option A.

Step-by-step explanation:

The student has asked to indicate the formula for C(n, r), which represents the number of combinations or ways to choose r items from a set of n distinct items without regard to the order of selection. The correct formula for this is given by option A, which is:

C(n, r) = n! / (r! * (n-r)!)

This formula is derived from the principles of combinatorics and factorial calculations in mathematics. In this formula, n! denotes the factorial of n, which is the product of all positive integers up to n. The denominator has two parts: r! is the factorial of r, and (n-r)! is the factorial of the difference between n and r which normalizes the count for disregarding order.