Explain how generating functions can be used to find thenumber of ways in which postage of r cents can be pastedon an envelope using 3-cent, 4-cent, and 20-cent stamps.a) Assume that the order the stamps are pasted on doesnot matter.b) Assume that the order in which the stamps are pastedon matters.c) Use your answer to part (a) to determine the numberof ways 46 cents of postage can be pasted on an envelopeusing 3-cent, 4-cent, and 20-cent stamps whenthe order the stamps are pasted on does not matter.(Use of a computer algebra program is advised.)d) Use your answer to part (b) to determine the numberof ways 46 cents of postage can be pasted in a row onan envelope using 3-cent, 4-cent, and 20-cent stampswhen the order in which the stamps are pasted on matters.(Use of a computer algebra program is advised.)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Explain how generating functions can be used to find the
number of ways in which postage of r cents can be pasted
on an envelope using 3-cent, 4-cent, and 20-cent stamps.
a) Assume that the order the stamps are pasted on does
not matter.
b) Assume that the order in which the stamps are pasted
on matters.
c) Use your answer to part (a) to determine the number
of ways 46 cents of postage can be pasted on an envelope
using 3-cent, 4-cent, and 20-cent stamps when
the order the stamps are pasted on does not matter.
(Use of a computer algebra program is advised.)
d) Use your answer to part (b) to determine the number
of ways 46 cents of postage can be pasted in a row on
an envelope using 3-cent, 4-cent, and 20-cent stamps
when the order in which the stamps are pasted on matters.
(Use of a computer algebra program is advised.)
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