[Guest]

Determine the probability that a number randomly drawn from the row of Pascal's Triangle having precisely 128 numbers is divisible by the 127^th number (reading left to right) in that row.

[superprismatic]

126 of the 128 are divisible by 127 (the

127^th entry counting from the left).

So, the probability that a randomly drawn

element is divisible by it is 63/64.

[Guest]

127 is prime. Thus all terms in that row will be divisible by 127

[superprismatic]

127 is prime. Thus all terms in that row will be divisible by 127

Of course...

For any prime P, (P Choose A) will always have a factor of P with the exception of the two values where A=0 and A=P.