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In Exercises 11–16, a die is rolled. Find the probability of getting a number greater than 4.
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Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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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 15
Use the formula for nCr to evaluate each expression. 5C0
Guida verificata passo dopo passo1
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.
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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.
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5:22
Combinations
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.
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5:22Factorials
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.
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5:22Combinations
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