Lab: More Counting

Notes:

• Same groups as Tuesday
• Finish Tuesday’s Lab if you haven’t
• Additional Problems (submit through problem 4 at a minimum)

1. Prove $n\choose k$=$n\choose n-k$
2. Given 24 CSC-151 Students, how many ways are there to arrange the students into 8 groups of size 3?
3. How Many License Plates with 3 letters followed by 3 numbers (In the US) are possible?
4. How many License Plates are possible if the letters and numbers can be in any order?
5. Prove that $n\choose k$=$n-1\choose k-1$+$n-1 \choose k$ (Pascal)
6. Prove that $(x+y)^k=\sum_{i=1}^n {}$ $n\choose i$ $x^iy^{n-i}$ (Binomial Expansion)