Find n and r if (a) ^n Cr=120, ^n Cr=20 (b) ^n Cr-1: ^n Cr ^n Ce, 1=2: 3: 4

Name: Problem 8, Chapter 3: Business Mathematics and Statistics
Uploaded: 2020-06-05T08:09:22-08:00
Duration: 56 s
Channel: Ankit Gupta
Description: Find n and r if (a) ^n Cr=120, ^n Cr=20 (b) ^n Cr-1: ^n Cr ^n Ce, 1=2: 3: 4

step 1 Question is asking that find the value of n factorial divided by n minus r factorial where n is

Find n and r if (a) ^n Cr=120, ^n Cr=20 (b) ^n Cr-1: ^n Cr...

Key Concepts

Binomial Coefficient

A binomial coefficient, often denoted as nCr, represents the number of ways to choose r elements from a set of n distinct items without regard to order. It is defined by the formula n!/(r!(n?r)!) and is a central concept in combinatorics, with applications ranging from probability theory to algebra and number theory.

Factorial Function

The factorial function, notated as n!, is the product of all positive integers less than or equal to n. It plays a crucial role in defining binomial coefficients and appears in many formulas in combinatorial calculations, such as those involving permutations and combinations.

Ratios of Consecutive Binomial Coefficients

When dealing with ratios of successive binomial coefficients, such as nC(r?1), nCr, and nC(r+1), a useful property is that nC(r+1)/nCr equals (n?r)/(r+1). This relationship helps simplify problems where the coefficients are given in a specific ratio, allowing one to set up equations and solve for unknown parameters.

Properties of Pascal’s Triangle

Pascal’s Triangle is a geometric arrangement of binomial coefficients where each number is the sum of the two directly above it. Its symmetry and recursive properties provide intuitive relationships between consecutive coefficients, which are instrumental in solving problems involving ratios or identities involving binomial coefficients.

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