Solution Found!
Solution: Prove that
Chapter 1, Problem 8TE(choose chapter or problem)
Prove that
\(\begin{aligned} \left(\begin{array}{c} n+m \\ r \end{array}\right)=&\left(\begin{array}{l} n \\ 0 \end{array}\right)\left(\begin{array}{c} m \\ r \end{array}\right)+\left(\begin{array}{c} n \\ 1 \end{array}\right)\left(\begin{array}{c} m \\ r-1 \end{array}\right) +\cdots+\left(\begin{array}{c} n \\ r \end{array}\right)\left(\begin{array}{c} m \\ 0 \end{array}\right) \end{aligned} \)
Hint: Consider a group of n men and m women. How many groups of size r are possible?
Questions & Answers
QUESTION:
Prove that
\(\begin{aligned} \left(\begin{array}{c} n+m \\ r \end{array}\right)=&\left(\begin{array}{l} n \\ 0 \end{array}\right)\left(\begin{array}{c} m \\ r \end{array}\right)+\left(\begin{array}{c} n \\ 1 \end{array}\right)\left(\begin{array}{c} m \\ r-1 \end{array}\right) +\cdots+\left(\begin{array}{c} n \\ r \end{array}\right)\left(\begin{array}{c} m \\ 0 \end{array}\right) \end{aligned} \)
Hint: Consider a group of n men and m women. How many groups of size r are possible?
ANSWER:Step 1 of 2
(a)
We are asked to give an analytic proof of the following equation.
Selecting object from total
objects.