How many ways can we list the names Bobby, Billy, Mickey, Sally, Betty, Jimmy, Mary, and Fred?
It would be 8! because one name can go in 8 different positions, another one can go in 7 different positions, another in 6, and so on.
And, 8!=40320
The question simply becomes, in how many ways can you arrange 8 different items ?
You MUST know how to do this if you are studying the topic of combinations and permutations.
To find the number of ways we can list the names, we can use the concept of permutations. Since we have 8 names, we can arrange them in 8! (8 factorial) ways.
To calculate 8!, we multiply all the numbers from 8 down to 1.
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
So, there are 40,320 ways we can list the names Bobby, Billy, Mickey, Sally, Betty, Jimmy, Mary, and Fred.
To determine the number of ways we can list the names Bobby, Billy, Mickey, Sally, Betty, Jimmy, Mary, and Fred, we can use the concept of permutations.
Permutations refer to the different arrangements or orders in which a set of objects can be placed. In this case, each name represents an object, and we want to find the number of possible arrangements of these objects.
The formula to find the number of permutations of a set of objects is given by:
n! / (n-r)!
where n is the total number of objects and r is the number of objects to be arranged.
In our case, we have 8 names to arrange (Bobby, Billy, Mickey, Sally, Betty, Jimmy, Mary, and Fred). Therefore, n = 8.
Let's calculate the number of permutations for different values of r:
When r = 8:
8! / (8-8)! = 8!
When r = 7:
8! / (8-7)! = 8!
When r = 6:
8! / (8-6)! = 8!
When r = 5:
8! / (8-5)! = 8!
When r = 4:
8! / (8-4)! = 8!
When r = 3:
8! / (8-3)! = 8!
When r = 2:
8! / (8-2)! = 8!
When r = 1:
8! / (8-1)! = 8!
By calculating the above expressions, we find that the number of ways to list the names Bobby, Billy, Mickey, Sally, Betty, Jimmy, Mary, and Fred is equal to 40,320, which is the value of 8!.
Therefore, there are 40,320 ways to arrange the given names.