Chapter 6: Q25E (page 430)
Show that and are logically equivalent
logically equivalent.
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How many ways are there to choose items from distinct items when
a) the items in the choices are ordered and repetition is not allowed?
b) the items in the choices are ordered and repetition is allowed?
c) the items in the choices are unordered and repetition is not allowed?
d) the items in the choices are unordered and repetition is allowed?
Find the number of 5-permutations of a set with nine elements.
a) Let nand rbe positive integers. Explain why the number of solutions of the equationwhereis a nonnegative integer forrole="math" localid="1668688407359" equals the number of r-combinations of a set with nelements.
b) How many solutions in nonnegative integers are there to the equationrole="math" localid="1668688467718" ?
c) How many solutions in positive integers are there to the equation in part (b)?
How many bit strings of length \({\rm{10}}\) over the alphabet \({\rm{\{ a,b,c\} }}\) have either exactly three \({\rm{a}}\)s or exactly four \({\rm{b}}\)s?
What is the coefficient of?
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