/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 1074 Find the value of \(\mathrm{C}(\... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 34: Problem 1074

Find the value of \(\mathrm{C}(\mathrm{n}, 0)\).

Short Answer

Expert verified
The value of \(\mathrm{C}(\mathrm{n}, 0)\) is always 1, regardless of the value of n.

Step by step solution

01

Recall the formula for combinations

The formula for combinations is given by \(\mathrm{C}(\mathrm{n}, \mathrm{k})=\frac{\mathrm{n}!}{\mathrm{k}!(\mathrm{n}-\mathrm{k})!}\), where \(\mathrm{n}!\) represents the factorial of n (the product of all the positive integers less than or equal to n).
02

Substitute the value of k

Since we want to find the value of \(\mathrm{C}(\mathrm{n}, 0)\), substitute "0" for k in the formula: \(\mathrm{C}(\mathrm{n}, 0)=\frac{\mathrm{n}!}{0!(\mathrm{n}-0)!}\).
03

Simplify the expression

Recall that 0! = 1, so the formula becomes: \(\mathrm{C}(\mathrm{n}, 0)=\frac{\mathrm{n}!}{1*(\mathrm{n}-0)!}\). As \(\mathrm{n}-0=\mathrm{n}\), the formula can be written as: \(\mathrm{C}(\mathrm{n}, 0)=\frac{\mathrm{n}!}{1*(\mathrm{n})!}\).
04

Evaluate the expression

The expression now simplifies to: \(\mathrm{C}(\mathrm{n}, 0)=\frac{\mathrm{n}!}{\mathrm{n}!}\). Since the factorial of any number divided by the same factorial is 1, the combination expression evaluates to: \(\mathrm{C}(\mathrm{n}, 0)=1\). So, the value of \(\mathrm{C}(\mathrm{n}, 0)\) is always 1, regardless of the value of n.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

How many groups can be formed from ten objects taking at least three at a time?

From 7 Englishmen and 4 Americans a committee of 6 is to be formed; in how many ways can this be done, (1) when the committee contains exactly 2 Americans, (2) at least 2 Americans?

How many four-letter "words" (we use "word" to mean any sequence of letters) which begin and end with a vowel may be formed from the letters \(\mathrm{a}, \mathrm{e}, \mathrm{i}, \mathrm{p}, \mathrm{q}\). (a) if no repetitions are allowed? (b) if repetitions are allowed?

A man and his wife decide to entertain 24 friends by giving 4 dinners with 6 guests each. In how many ways can the first group be chosen?

A boy has in his pocket a penny, a nickel, a dime, and a quarter. How many different sums of money can he take out if he removes one or more coins?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.