Total Number of all r-Combinations of n Objects. — Suppose all the combinations of
n objects taken one at a time (the
number of the objects) are found, and then all the combinations taken two at a time, then all those three at a
time, and
so on until all those taken n at a time (all at once) are formed. How many
combinations will there be
altogether?
— J.E. Thompson, Algebra for the Practical Man (D. Van Nostrand, 1946)
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