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hen a falling marble strikes a peg, it will either bounce left or right. Galton's motivation was to study the final distribution of marbles amongst the bins.

Consider a quincunx with only $3$ rows of pegs.

a$.$ Draw this quincunx and label the bins starting with zero on the far left.

b$.$ How many bins does it have to catch the marbles?

c$.$ Count the number of different paths a marble could take to eventually land in bin $2.$ How many are there?

d$.$ How many different paths to land in bin $1?$

e$.$ How many paths to land in bin $0?$

f$.$ How many paths to land in bin $3?$

g$.$ How many total paths are there?