1971 AMC 12 Question 24 - thichhoctoan.com

Question 24

Pascal’s triangle is an array of positive integers, shown below, in which the first row is $1,$ the second row is two $1$’s, each row begins and ends with $1,$ and each other entry is the sum of the two entries above it.

Question illustration

The quotient of the number of entries in the first $n$ rows which are not $1$’s and the number of $1$’s is:

$\dfrac{n^2-n}{2n-1}$
$\dfrac{n^2-n}{4n-2}$
$\dfrac{n^2-2n}{2n-1}$
$\dfrac{n^2-3n+2}{4n-2}$
None of these