Joey finds that a number in a certain row of Pascal’s Triangle can be found using combinations. For example, the 8th number in row 14 is 13C7. Determine algebraically the row of Pascal’s Triangle that will have 91 as the third number

Question

Joey finds that a number in a certain row of Pascal’s Triangle can be found using combinations.  For example, the 8th number in row 14 is 13C7.  Determine algebraically the row of Pascal’s Triangle that will have 91 as the third number

mertsj · Answer

90C6

anonymous · Answer

what? can u show me the steps?

anonymous · Answer

Let n be the row of pascals triangle. Since the third term of the row must be 91, we have that nC2 must equal 91.  This gives us an equation:$$\left(\begin{matrix}n \ 2\end{matrix}\right)=91\iff \frac{n(n-1)}{1\cdot 2} = 91\iff n(n-1) = 182$$Solve this equation for n and you will have your answer.

anonymous · Answer

It comes down to knowing how to calculate nCk.  How comfortable are you with the formulas?