Explain how generating functions can be used to find thenumber of ways in which postage of r cents can be pastedon an envelope using 2-cent, 7-cent, 13-cent, and 32-centstamps.a) Assume that the order the stamps are pasted on doesnot matter.b) Assume that the order the stamps are pasted on matters.c) Use your answer to part (a) to determine the numberof ways 49 cents of postage can be pasted on an envelopeusing 2-cent, 7-cent, 13-cent, and 32-cent stampswhen 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 ofways 49 cents of postage can be pasted on an envelopeusing 2-cent, 7-cent, 13-cent, and 32-cent stamps whenthe order in which the stamps are pasted on matters. (Useof a computer algebra program is advised.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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 2-cent, 7-cent, 13-cent, and 32-cent
stamps.
a) Assume that the order the stamps are pasted on does
not matter.
b) Assume that the order the stamps are pasted on matters.
c) Use your answer to part (a) to determine the number
of ways 49 cents of postage can be pasted on an envelope
using 2-cent, 7-cent, 13-cent, and 32-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 49 cents of postage can be pasted on an envelope
using 2-cent, 7-cent, 13-cent, and 32-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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