(Solved): Read all carefully and use matlab to answer Problem 3.7 Pascal's triangle, shown below, is a method ...

Problem $$3.7$$ Pascal's triangle, shown below, is a method for visualizing the binomial coefficients *. These coefficients may be written as $$\left(\begin{array}{l}n\\ k\end{array}\right),{}_n{C}_{kr}\text{ or }C(n,k)$$ where $$n$$ is the row number and $$k$$ is the column number (starting with $$n=0$$ and $$k=0$$ ). Left-aligned Pascal's triangle (as an array) One way to calculate each binomial coefficient is to add the two numbers above it. That is: - $$C(0,0)=1$$ (by definition) - For row $$n$$ (where $$n?1$$ ): $$C(n,1)=1$$ - $$C(n,k)=C(n?1,k?1)+C(n?1,k)$$ for $$k=\{2,3,\dots ,n\}$$ - $$C(n,k)=0$$ for all other values (that is, for $$k>n$$ ) Write a MATLAB code to create an array containing Pascal's triangle (left-aligned) for rows $$n=0$$ to $$n=10$$ using nested FOR loops, then display the array. (Hint: Remember that array indices in MATLAB start at 1. You will have to adjust the formulas in your code to account for this.) *These coefficients show up frequently in probability and in polynomials. For example, when expanding $$(x+y{)}^5=x^5+5x^{4}y+10x^3{y}^2+10x^2{y}^3+5x{y}^4+y^5$$ the coefficients of the terms after expanding are the binomial coefficients for $$n=5$$. Or, suppose we purchase bolts where each bolt has a 1 in 20000 chance of being faulty. If we select 5000 bolts at random, the probability that exactly $$k$$ bolts are faulty is $$P(k\text{ faulty })=C(5000,k)?{\left(\frac{1}{20000}\right)}^k?{\left(\frac{19999}{20000}\right)}^{5000?k}?100\%$$ Pascal's triangle is named for $$17^{\text{th }}$$-century French mathematician Blaise Pascal, but the triangle had already been in use for several centuries in several parts of the globe (including Europe) before Pascal's time.