## The Binomial Expansion

**Note**: This is the second part of the Binomial Expansion Series

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Part I: Milkshakes, Beads, and Pascal’s Triangle

Part II: Binomial Expansion

In the Milkshakes, Beads, and Pascal’s Triangle article, we have shown that the combination of the binary numbers 1 and 0 may be interpreted as the number the flavors of milk shakes, or the number of possible paths of the bead in our Galton board as shown in Table 1. Recall that in the Milkshake problem, Issa was given a choice to combine any number of flavors from four fruits: Apple, Banana, Chico and Durian. Thus, 0101 means banana-durian milkshake. On the other hand, in the beads problem, 0101 is LRLR or the bead went to the left after hitting the peg in row ** A**, right in after hitting the peg in row

**, left after hitting the peg in row**

*B***and right after hitting the peg in row**

*C***. » Read more**

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