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An element is randomly chosen from among the first 15 rows of Pascal's Triangle. What is the probability that the value of the element chosen is 10?

 

Note: The 1 at the top is often labelled the "zeroth" row of Pascal's Triangle, by convention. So to count a total of 15 rows, use rows 0 through 14.

 Dec 17, 2020
 #1
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"10"  appears 4 times  in the rows 0 - 14  inclusive

 

The number of  elements  in the first  n  rows  = (n + 1) (n + 2)  /  2 

 

So....the number of elements  =   (14 + 1) (14 + 2)   / 2   =   15 * 8    = 120

 

So

 

P(10)  =   4 / 120    =   1   /  30 

 

 

cool cool cool

 Dec 17, 2020

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