Evaluate each of the following expressions. a) ( 7 3 )+( 7 4 ) b) ( 8

Name: Problem 3, Chapter 4: Higher Level Mathematics
Uploaded: 2020-03-29T18:33:52-08:00
Duration: 1 min 20 s
Channel: Julian Wong
Description: Evaluate each of the following expressions. a) ( 7 3 )+( 7 4 ) b) ( 8 4 ) c) ( 10 6 )+( 10 7 ) d) ( 11 7 )

step 1 We're being asked to evaluate the following expressions. Again, this is the combination notation

Question

Evaluate each of the following expressions. a) $\left(\begin{array}{l}7 \\ 3\end{array}\right)+\left(\begin{array}{l}7 \\ 4\end{array}\right)$ b) $\left(\begin{array}{l}8 \\ 4\end{array}\right)$ c) $\left(\begin{array}{l}10 \\ 6\end{array}\right)+\left(\begin{array}{l}10 \\ 7\end{array}\right)$ d) $\left(\begin{array}{l}11 \\ 7\end{array}\right)$

   Evaluate each of the following expressions.
a) $\left(\begin{array}{l}7 \\ 3\end{array}\right)+\left(\begin{array}{l}7 \\ 4\end{array}\right)$
b) $\left(\begin{array}{l}8 \\ 4\end{array}\right)$
c) $\left(\begin{array}{l}10 \\ 6\end{array}\right)+\left(\begin{array}{l}10 \\ 7\end{array}\right)$
d) $\left(\begin{array}{l}11 \\ 7\end{array}\right)$

Higher Level Mathematics

Ibrahim Wazir, Tim… 2012 Edition

Chapter 4, Problem 3

Instant Answer

Solved by Expert Julian Wong

03/29/2020

Step 1

This is the combination notation, also known as "n choose r", which represents the number of ways to choose r elements from a set of n elements. Show more…

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Evaluate each of the following expressions. a) $\left(\begin{array}{l}7 \\ 3\end{array}\right)+\left(\begin{array}{l}7 \\ 4\end{array}\right)$ b) $\left(\begin{array}{l}8 \\ 4\end{array}\right)$ c) $\left(\begin{array}{l}10 \\ 6\end{array}\right)+\left(\begin{array}{l}10 \\ 7\end{array}\right)$ d) $\left(\begin{array}{l}11 \\ 7\end{array}\right)$

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Key Concepts

Binomial Coefficients

Binomial coefficients, typically expressed as (n choose k), count the number of ways to choose k elements from a set of n elements without regard to order. They form the building blocks in combinatorics and have numerous applications including probability theory and algebra, such as in the expansion of a binomial expression using the Binomial Theorem.

Pascal's Rule

Pascal's Rule, also known as the recursive formula for binomial coefficients, states that (n choose k) is equal to (n-1 choose k-1) plus (n-1 choose k). This identity is central to Pascal's Triangle and is used to compute binomial coefficients recursively, often simplifying the evaluation of sums of binomial coefficients.

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