Chapter 6: Q5E (page 421)
How many terms are there in the expansion ofafter like terms are collected?
After like terms are collected there are 101 terms in the expression.
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What is the coefficient ofin the expansion of
6. How many ways are there to select five unordered elements from a set with three elements when repetition is allowed?
Let\(n\)and \(k\) be integers with \(1 \le k \le n\). Show that
\(\sum\limits_{k = 1}^n {\left( {\begin{array}{*{20}{l}}n\\k\end{array}} \right)} \left( {\begin{array}{*{20}{c}}n\\{k - 1}\end{array}} \right) = \left( {\begin{array}{*{20}{c}}{2n + 2}\\{n + 1}\end{array}} \right)/2 - \left( {\begin{array}{*{20}{c}}{2n}\\n\end{array}} \right)\)
Let. S = {1,2,3,4,5}
a) List all the 3-permutations of S.
b) List all the 3 -combinations of S.
There are six different candidates for governor of a state. In how many different orders can the names of the candidates be printed on a ballot?
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