A coordinator will select 4
songs from a list of 14
songs to compose an event's musical entertainment lineup. How many different lineups are possible?
The number of different lineups that are possible can be calculated using the combination formula:
nCr = n! / r!(n-r)!
Where n is the total number of songs (14) and r is the number of songs to be selected (4).
14C4 = 14! / 4!(14-4)!
14C4 = 14! / 4!10!
14C4 = (14 x 13 x 12 x 11) / 4 x 3 x 2 x 1
14C4 = 43,680 / 24
14C4 = 1,820
Therefore, there are 1,820 different possible lineups that can be composed from the list of 14 songs.