Chapter 6: Q45E (page 397)
How many sections of size \(34\) are needed to accommodate all the students?
\(40\) sections are needed to accommodate all the students.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
The row of Pascal's triangle containing the binomial coefficients, is:
Use Pascal’s identity to produce the row immediately following
this row in Pascal’s triangle.
Let\(n\)and \(k\) be integers with \(1 \le k \le n\). Show that
\(\sum\limits_{k = 1}^n {\left( {\begin{array}{*{20}{l}}n\\k\end{array}} \right)} \left( {\begin{array}{*{20}{c}}n\\{k - 1}\end{array}} \right) = \left( {\begin{array}{*{20}{c}}{2n + 2}\\{n + 1}\end{array}} \right)/2 - \left( {\begin{array}{*{20}{c}}{2n}\\n\end{array}} \right)\)
How many bit strings of length \({\bf{10}}\) have
a) exactly three \(0s\)?
b) more \(0s\) than \(1s\) ?
c) at least seven \(1s\) ?
d) at least three \(1s\) ?
A test containstrue/false questions. How many different ways can a student answer the questions on the test, if answers may be left blank?
Show that if \(p\) is a prime and\(k\)is an integer such that \(1 \le k \le p - 1\), then \(p\)divides \(\left( {\begin{array}{*{20}{l}}p\\k\end{array}} \right)\).
What do you think about this solution?
We value your feedback to improve our textbook solutions.
