Binomial Expansion

Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to find the largest or smallest possible coefficient of the third term in the expansion.


(The expansion must have at least three terms.)
Consider Pascal’s Triangle.
How many different ways can you arrive at your answer for the smallest possible?


Largest possible: 3,699,376,128
Smallest possible: 1
Number of ways to get the smallest possible: 7

Source: Dana Harrington

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