Domanda del libro di testo
In Exercises 23–28, evaluate each factorial expression. (2n+1)!/(2n)!
587
views
Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 9, Problema 27
Evaluate each expression.
Guida verificata passo dopo passo1
Identify the components of the expression: \(\frac{4C2 \cdot 6C1}{18C3}\). Here, \(nCr\) represents the combination formula, which calculates the number of ways to choose \(r\) items from \(n\) items without regard to order.
Recall the combination formula: \(nCr = \frac{n!}{r! (n-r)!}\), where \(n!\) denotes the factorial of \(n\).
Calculate each combination separately using the formula:
- Calculate \(4C2 = \frac{4!}{2! (4-2)!}\)
- Calculate \(6C1 = \frac{6!}{1! (6-1)!}\)
- Calculate \(18C3 = \frac{18!}{3! (18-3)!}\)
Substitute the calculated values of \$4C2\(, \)6C1$, and \$18C3$ back into the original expression \(\frac{4C2 \cdot 6C1}{18C3}\).
Simplify the resulting fraction by multiplying the numerator values and then dividing by the denominator value to get the final simplified expression.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
5mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Combination Formula
The combination formula, denoted as nCr, calculates the number of ways to choose r items from n without regard to order. It is given by nCr = n! / [r!(n-r)!], where '!' denotes factorial. This concept is essential for evaluating expressions involving combinations.
Video consigliato:
5:22
Combinations
Factorials
Factorials represent the product of all positive integers up to a given number n, written as n!. They are fundamental in calculating permutations and combinations, as they help determine the total number of arrangements or selections.
Video consigliato:
5:22Factorials
Simplifying Algebraic Fractions
Simplifying algebraic fractions involves reducing expressions by factoring and canceling common terms. This skill is crucial when evaluating complex expressions like the given combination formula multiplied and divided by other terms.
Video consigliato:
05:07Simplifying Algebraic Expressions
Pratica correlata
Domanda del libro di testo
Use mathematical induction to prove that each statement is true for every positive integer n. 6 is a factor of n(n + 1)(n + 2).
691
views
Domanda del libro di testo
Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for an to find a20, the 20th term of the sequence. a1 = 9, d=2
974
views
Domanda del libro di testo
Evaluate each factorial expression. (n+2)!/n!
888
views
Domanda del libro di testo
Use the Binomial Theorem to expand each binomial and express the result in simplified form. (3x − y)5
706
views
Domanda del libro di testo
Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the sum of the first 11 terms of the geometric sequence: 3, - 6, 12, - 24, ...
945
views