Question

Find the value of each combination. $$30^{C_{4}}$$

   Find the value of each combination.
$$30^{C_{4}}$$

Statistics Informed Decisions Using Data

Statistics Informed Decisions Using Data

Michael Sullivan III 4th Edition

Chapter 5, Problem 26

Instant Answer

Solved by Expert Narayan Hari

03/15/2021

Step 1

The formula for combination is given by $n^{C_{r}} = \frac{n!}{r!(n-r)!}$ where $n$ is the total number of items, $r$ is the number of items to choose, and $!$ denotes factorial. Show more…

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Find the value of each combination. $$30^{C_{4}}$$

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Key Concepts

Combination (Binomial Coefficient)

A combination is a selection of items from a larger set where the order does not matter. The binomial coefficient, often written as C(n, r) or n choose r, represents the number of ways to choose r elements from a set of n elements. It is fundamental in combinatorics and probability, and is given by the formula n! / (r! (n - r)!), where n! denotes the factorial of n.

Factorial

The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Factorials are essential in combinatorial formulas because they account for the total number of arrangements of objects. They are used in the calculation of combinations and permutations to simplify expressions involving large numbers.

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