Question

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

Answer 1

There are 3003 possible lineups that can be formed from the 14 bands.

Step-by-step explanation:

In order to determine the number of possible lineups, we need to use the concept of combinations. We have 14 bands and we need to choose 6 of them. The formula for combinations is given by nCr = n! / (r!(n-r)!), where n represents the total number of items and r represents the number of items to be chosen.

Plugging in the values for this problem, we have 14C6 = 14! / (6!(14-6)!). Simplifying further, we get 14C6 = (14 x 13 x 12 x 11 x 10 x 9) / (6 x 5 x 4 x 3 x 2 x 1).

Calculating this expression, we find that 14C6 = 3003. Therefore, there are 3003 possible lineups that can be formed from the 14 bands.

Answer 2

There are 2,162,160 possible combination that could be made if there are 14 bands and only 6 slots available. This is computed using factorial. By using factorial we first need to identify the number of band and the number of slots available. It could be express as 14! - 8! or 14 x 13 x 12 x 11 x 10 x 9, which is equal to 2,162,160 combination.