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Binomial Theorem Quiz

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Questions and Answers

Which term in the expansion of $(x + y)^n$ contains the binomial coefficient?

$by^n$
$ax^by^{n-b}$ (correct)
$ax^{n-b}y^b$
$ax^n$

What is the relationship between the exponents $b$ and $c$ in the expansion of $(x + y)^n$?

$b - c = n$
$b + c = n$ (correct)
$b = c$
$b imes c = n$

What is the binomial coefficient in the term $ax^2y^3$?

$2$
$a$
$3$
$5$ (correct)

What does the binomial coefficient represent in combinatorics?

<p>The number of different combinations of $b$ elements that can be chosen from an $n$-element set (A)</p> Signup and view all the answers

What is another name for the binomial coefficient?

<p>The combination coefficient (D)</p> Signup and view all the answers

Flashcards

Binomial term structure

The term in the expansion of $(x + y)^n$ is $ax^by^{n-b}$.

Exponents relationship

In the expansion of $(x + y)^n$, the exponents $b$ and $c$ satisfy $b + c = n$.

Binomial coefficient in $ax^2y^3$

The binomial coefficient for the term $ax^2y^3$ is 5.

Meaning of binomial coefficient

In combinatorics, it represents the number of ways to choose $b$ elements from an $n$-element set.

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Another name for binomial coefficient

The binomial coefficient is also called the combination coefficient.