Probability
# Binomial Theorem

What positive integer $n$ satisfies ${{n+2} \choose 11}=109 \cdot {n \choose 9}?$

What is the value of positive integer $n$ satisfying ${26 \choose n}={26 \choose {n-4}}?$

If ${n+4 \choose 2}+{n+3 \choose 2}=25,$ what is the value of $n?$