Example — Cross-country race

Example — Cross-country: choosing groups

In a class there are $8$ boys and $13$ girls; the PE teacher must choose $3$ boys and $5$ girls for the cross-country race. In how many ways can he do it?

The “boys” and “girls” choices are independent, so by the counting principle the total number of ways is the product of the ways for each choice. The order within each group does not matter (a subset is formed), so they are simple combinations:

$\binom{8}{3}\cdot \binom{13}{5} = 56\cdot 1287 = 72\,072.$

Links

Topics: Probability
Concepts: Simple combinations · Counting principle
Methods: Simple combinations · Counting principle
Skills: Combinatorial calculus