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Fixed Row, Random Draw (Posted on 2010-05-14) Difficulty: 1 of 5
Determine the probability that a number randomly drawn from the row of Pascal's Triangle having precisely 128 numbers is divisible by the 127th number (reading left to right) in that row.

No Solution Yet Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

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Solution 2 easy, we try harder | Comment 2 of 5 |

127 being prime,all coefficients in the 128 th row,safe the first and the last, will be divisible by 127.

So, out of 128 coefficients, 126 qualify and   p=126/128=98.44%.<br>

The problem would be more challenging if 127 were replaced by a composite number, high enough to preclude finger counting,say 5^4=625, and the row would be 626th.

Then one should devise a method of counting the highest power of 5 in the dividers of each coefficient..<br>.<br>

Any volunteers?

BTW, why left to right?

 

Edited on May 14, 2010, 3:07 pm
  Posted by Ady TZIDON on 2010-05-14 15:03:50

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