*Challenge question #8 (25/04/2016)*

**Junior Question**

A group of $16$ girls is randomly divided into $4$ groups of $4$. What is the probability that four friends Amy, Beth, Caitlin, and Donna are all placed in different groups?

**Senior Question**

Show that $\frac{1}{2}\times\frac{3}{4}\times\frac{5}{6}\times\frac{7}{8}\times$ .... $\times\frac{99}{100}<\frac{1}{10}$.