Chapter 6: Q7E (page 413)
Find the number of 5-permutations of a set with nine elements.
The resultant answer is 15,20..
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What is the coefficient ofin the expansion of
a) State the pigeonhole principle.
b) Explain how the pigeonhole principle can be used to show that among any 11 integers, at least two must have the same last digit.
How many permutations of the letters \(ABCDEFG\) contain
a) the string \(BCD\)?
b) the string \(CFGA\)?
c) the strings \(BA\) and \(GF\)?
d) the strings \(ABC\)and \(DE\)?
e) the strings \(ABC\)and \(CDE\)?
f) the strings \(CBA\)and \(BED\)?.
a) What is the difference between an r-combination and an r-permutation of a set with n elements?
b) Derive an equation that relates the number of r-combinations and the number of r-permutations of a set with n elements.
c) How many ways are there to select six students from a class of 25 to serve on a committee?
d) How many ways are there to select six students from a class of 25 to hold six different executive positions on a committee?
5. How many ways are there to assign three jobs to five employees if each employee can be given more than one job?
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