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)=(n!)/(p!(n-p)!)`

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

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

Therefore there are 55 lineups possible.