A math question about pascal's triangle. NEED help!!!?

Question

In Pascal's triangle, find the ratio of the numbers in the first 50 rows that are not 1s divided by the number of 1s in the first 50 rows. Answer as a fraction in lowest terms.

Answer 1

The previous answerer is correct as far as he went, but he did not answer your question. The total number of numbers in the first 50 rows is indeed 51*50/2 = 1275, because the sum of integers 1 to n is (n + 1)*n/2. The number of 1's in the first 50 rows is 1 in the first row and 2 in each of rows 2 through 50, so that's 1 + 49*2 = 99. That means that the number of non-1's is 1275 - 99 = 1176. So the ratio of non-1's to 1's is 1176 / 99, which can be simplified to 392 / 33 by dividing through by 3.

Answer 2

In each row there's a 1 on each end. This comes from

nC0 = nCn = 1

Rows and columns are both numbered from 0.

So, row 0 has one 1
rows 1 though 49 have 2 ones each.


That's a start.

David's answer is good except note that the first 50 rows would be numbered 0 though 49.

Answer 3

Each row has one more number than the previous row. Therefore, the total number of numbers is the sum of the first 50 integers, which can be expressed as 51*50/2