Question 8

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?

Answer

The probability is $\frac{64}{455}$.

Worked Solution

Senior Question

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

Hint

Compare the product with $\frac{2}{3}\times\frac{4}{5}\times\frac{6}{7}\times$ .... $\times\frac{98}{99}$.

Worked Solution