Answered

IDNLearn.com: Where your questions meet expert advice and community insights. Ask your questions and get detailed, reliable answers from our community of knowledgeable experts.

Ay benefit concert, twelve bands have volunteered to perform but there is only enough time for eight of the bands to play. How many lineups are possible?

Sagot :

Facundo3141592idn

Answer:

There are 495 different lineups

Step-by-step explanation:

If we have a set of N elements, the total number of different combinations of K elements (such that K ≤ N) is given by:

[tex]C (N, K) = \frac{N!}{(N - K)!*K!}[/tex]

In this case, we have 12 bands, but we can only select 8 of them.

Then we have N = 12, and K = 8.

Using the above formula, we can conclude that the total number of possible lineups (combinations of bands) is:

[tex]C (12, 8) = \frac{12!}{(12 - 8)!*8!} = \frac{12!}{(4)!*8!} = \frac{12*11*10*9}{4*3*2} = 495[/tex]

There are 495 different lineups

Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.