What is the value of 7^C2 ?

Name: Problem 76, Chapter 6: Algebra 2
Uploaded: 2019-08-28T03:24:06-08:00
Duration: 27 s
Channel: K B
Description: What is the value of 7^C2 ?

step 1 So in this question we're asked, what is the value of seven choose two? So first, we have to loo

Question

What is the value of $7^{\mathrm{C}}_{2} ?$

   What is the value of $7^{\mathrm{C}}_{2} ?$

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 6, Problem 76

Instant Answer

Solved by Expert K B

08/28/2019

Step 1

This is a combination formula, which is defined as $n^{\mathrm{C}}_{r} = \frac{n!}{r!(n-r)!}$, where $n$ is the total number of items, $r$ is the number of items to choose, and $!$ denotes factorial. Show more…

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What is the value of $7^{\mathrm{C}}_{2} ?$

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Key Concepts

Combinations

This concept deals with selecting items from a larger set where the order does not matter. In mathematics, combinations are used to calculate how many different groups can be formed by choosing a specific number of elements from a larger set, and they are often represented using the notation nCk.

Factorial

A factorial, denoted by the symbol '!', is the product of all positive integers up to a given number. It is a fundamental function in combinatorics for computing combinations and permutations, as it is used in the formula that determines the number of ways to arrange or select items.

Binomial Coefficient

The binomial coefficient is a key concept in combinatorics that represents the number of ways to choose k elements from an n-element set without considering the order. It is calculated using the formula nCk = n! / (k!(n-k)!), and it also appears in the expansion of a binomial raised to a power according to the binomial theorem.

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