From 56b740565fd6467564be28b5465ad24cccf71109 Mon Sep 17 00:00:00 2001 From: Holden Rohrer Date: Thu, 16 Jan 2020 21:24:46 -0500 Subject: moved comb hw --- tech-math/comb/ws1.tex | 31 +++++++++++++++++++++++++++++++ 1 file changed, 31 insertions(+) create mode 100644 tech-math/comb/ws1.tex (limited to 'tech-math/comb/ws1.tex') diff --git a/tech-math/comb/ws1.tex b/tech-math/comb/ws1.tex new file mode 100644 index 0000000..afb8374 --- /dev/null +++ b/tech-math/comb/ws1.tex @@ -0,0 +1,31 @@ +\input ws-form.tex + +{\bf \noindent\line{Math 3012-QHS \hfil Name: \rm \underline{Holden Rohrer}} +Fall 2019\par\noindent +Worksheet 1\par\noindent +Due 08/27/2019} +\smallskip \hrule \medskip +\question{ +Q1 - The Greek alphabet consists of 24 letters. How many five-character strings can be made using the Greek alphabet (ignoring the distinction between uppercase and lowercase)? +}{ +$24^5$ because the number of strings which can exist is the product of the number of the individual choices ($m = m_1\cdot m_2\ldots m_{n-1}\cdot m_n$), and each of the 5 individual choices has 24 options from the 24 letters. +} +\question{ +Q2 - Assume that a license plate consists of 3 Latin alphabet letters followed by 4 numerals. How many license plates are there such that the numerals are distinct from one another and the last numeral is less than 3? + +}{ +By a similar method, the alphabet letters have $26^3$ possibilities. The numerals can be treated as choosing 2 distinct objects (for the last numeral), then ${9!}\over{6!}$ for the other 3, the options having been reduced by whichever chosen as the last numeral. This gives a final enumeration of $26^3\cdot 2 \cdot 504 = 17,716,608$. +}\eject + +\question{ +Q3 - Twenty-three students compete in a math competition in which the top three students are recognized with trophies for first, second, and third place. How many different outcomes are there for the top three places? +}{ +$P(23,3)$ because order matters and there are three people chosen from twenty-three. +} + +\question{ +Q4 - Continuing the above problem---now assume that 3 additional students (distinct from the top 3) are awarded an honorable mention. How many different ways may non-placing students be awarded an honorable mention? +}{ +Order doesn't matter, and there are now only 20 students to choose, from so there are ${20 \choose 3}$ ways to choose honorable mentions. +}\eject +\bye -- cgit