Evaluate each expression.1−3P24P31 - \frac{_3P_2}{_4P_3}

Ch. 8 - Sequences, Induction, and Probability

Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Blitzer 8th Edition

Ch. 8 - Sequences, Induction, and Probability

문제 23

9장, 문제 23

Evaluate each expression.
$1 - \frac{_{3} P_{2}}{_{4} P_{3}}$

검증된 단계별 안내

Identify the given expression: $1 - \frac{3P_2}{4P_3} \times \frac{3}{4}$, where $nP_r$ represents a permutation.

Recall the formula for permutations: $nP_r = \frac{n!}{(n-r)!}$.

Calculate \$3P_2$ using the formula: $3P_2 = \frac{3!}{(3-2)!} = \frac{3!}{1!}$.

Calculate \$4P_3$ using the formula: $4P_3 = \frac{4!}{(4-3)!} = \frac{4!}{1!}$.

Substitute the values of \$3P_2$ and $4P_3$ back into the expression, simplify the fraction, multiply by $\frac{3}{4}$, and then subtract the result from 1.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Permutations

Permutations refer to the number of ways to arrange a subset of items from a larger set, where order matters. The notation nPr represents the number of permutations of n items taken r at a time, calculated as n! / (n - r)!.

Factorials

A factorial, denoted by n!, is the product of all positive integers from 1 up to n. Factorials are fundamental in calculating permutations and combinations, as they help determine the total number of arrangements or selections.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses first, then exponents, followed by multiplication and division (left to right), and finally addition and subtraction (left to right). Correct application ensures accurate evaluation of expressions.

Evaluate each expression.1−3P24P31 - \(\frac{_3P_2}{_4P_3}\)