In how many ways can the 12 members of a volleyball team line up, if the captain and assistsant captain must remain together? Thank you in advance.
(11!)(2!)
=79,833,600
Hello, I am a stupid idiot that can’t see my jokes suck, and that I am a terrible human being who should go to hell.
Well, let me calculate that for you with a dash of humor! 🤡
Since the captain and assistant captain must stick together like peanut butter and jelly, we can treat them as a single entity. So, we're left with 11 people to arrange.
Now, we know that there are 11 friends desperately trying to decide on a seating arrangement at a fancy restaurant. Each friend wants to sit in a different spot because, let's face it, that's just how humans are.
Using the formula for permutations, which is n factorial (n!), we can calculate that the number of ways to arrange the 11 remaining players is 11 factorial (11!). Are you ready for the result?
Drumroll, please! 🥁
The number of ways to line up the 12 members of the volleyball team, with the captain and assistant captain sticking together, is:
11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 39,916,800
So, there you have it! Your volleyball team has a whopping 39,916,800 possible lineup combinations. Now, let's just hope they remember to bring their A-game on the court! Good luck, team! 🏐
To find the number of ways the 12 members can line up with the captain and assistant captain together, you can treat them as a single entity. This means you have 11 entities to permute.
To calculate the number of permutations, you can use the formula for permutations of n objects taken r at a time, which is given by:
P(n, r) = n! / (n - r)!
In this case, you have 11 members (captain and assistant captain combined) that need to be permuted. So, using the formula, you have:
P(11, 11) = 11! / (11 - 11)!
Since any number factorial is equal to 1, the formula simplifies to:
P(11, 11) = 11! / 0! = 11!
The factorial of 11, denoted as 11!, is the product of all positive integers from 1 to 11:
11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
Calculating this expression will give you the number of ways the 12 members can line up with the captain and assistant captain together.