Give an example problem where you would use Permutation skills and formula to solve. Solve your example problem showing all your steps. (Hint: you could use an example from class or a previous quick check - DO NOT use one you find via google.)(3 points)
Example problem: In a group of 5 friends (Alice, Bob, Charlie, David, and Emily), they want to take a photo together. In how many ways can they arrange themselves in a line for the photo?
Solution:
To solve this problem, we can use the permutation formula:
\[P(n,r) = \frac{n!}{(n-r)!}\]
In this case, there are 5 friends, so n = 5. They want to arrange themselves in a line, so r = 5.
Plugging these values into the formula, we get:
\[P(5,5) = \frac{5!}{(5-5)!}\]
\[P(5,5) = \frac{5!}{0!}\]
Now, we need to calculate 5! (5 factorial) and 0! (0 factorial):
5! = 5 x 4 x 3 x 2 x 1 = 120
0! = 1
Plugging these values back into the formula, we get:
\[P(5,5) = \frac{120}{1}\]
\[P(5,5) = 120\]
Therefore, there are 120 ways for the 5 friends to arrange themselves in a line for the photo.
make it understandable with less formulas
Example problem: In a group of 5 friends (Alice, Bob, Charlie, David, and Emily), they want to take a photo together. In how many ways can they arrange themselves in a line for the photo?
Solution:
To solve this problem, we can think of it as arranging the 5 friends in a line. Since the order of the friends matters (Alice at the front is different from Alice at the back), we can use the concept of permutations.
We can imagine the first friend having 5 choices, the second friend having 4 choices (since one friend is already in the first position), the third friend having 3 choices, and so on.
So, the total number of ways to arrange the 5 friends is:
5 x 4 x 3 x 2 x 1 = 120
Therefore, there are 120 ways for the 5 friends to arrange themselves in a line for the photo.