Question

At a benefit concert, eleven bands have volunteered to perform but there is only enough time for nine of the bands to play. How many lineups are possible?

Answer 1

Since we have 11 options of bands and need to choose 9, the number of lineups possible is given by a combination of 11 choose 9.

The formula to calculate a combination of n choose p is given by:

$C(n,p)=\frac{n!}{p!(n-p)!}$

So, for n = 11 and p = 9, we have:

$\begin{gathered} C(11,9)=\frac{11!}{9!(11-9)!}\\ \\ =\frac{11\cdot10\cdot9!}{9!\cdot2!}\\ \\ =\frac{11\cdot10}{2}=55 \end{gathered}$

Therefore there are 55 lineups possible.