Use the formula for nCr to evaluate each expression. ₅C₀

검증된 단계별 안내

Recall the formula for combinations, which is given by $nCr = \frac{n!}{r!(n-r)!}$, where $n!$ denotes the factorial of $n$.

Identify the values of $n$ and $r$ from the expression \$5C0$, so here $n = 5$ and $r = 0$.

Substitute these values into the formula: $5C0 = \frac{5!}{0!(5-0)!} = \frac{5!}{0! \cdot 5!}$.

Simplify the factorial expressions, remembering that \$0!$ is defined as 1, so the expression becomes $\frac{5!}{1 \cdot 5!}$.

Cancel out the common factorial terms in the numerator and denominator to simplify the expression further.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Combination Formula (nCr)

The combination formula, denoted as nCr, calculates the number of ways to choose r elements from a set of n elements without regard to order. It is given by nCr = n! / [r! (n - r)!], where '!' denotes factorial. This formula is fundamental for counting problems in algebra and probability.

Factorial Function

The factorial of a non-negative integer n, written as n!, is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials are essential in calculating combinations and permutations, as they appear in the numerator and denominator of the nCr formula.

Evaluating Special Cases in Combinations

When evaluating combinations like nC0 or nCn, the result is always 1 because there is exactly one way to choose none or all elements from a set. Recognizing these special cases simplifies calculations and helps avoid unnecessary computation.

Use the formula for nCr to evaluate each expression. 5C0