Find the number of ways that 4 flags can be displayed on a flagpole, one above the other, if 10 different flags are available.
Since the order matters we use Permutation in a calculator it looks like nPr: the n flags arranged into r places.
in this case: 10 flags arranged into 4 places.
the top position would have 10 choices of flags
second position, 9 choices
third position, 8 choices
last position only seven choices.
10 * 9 * 8 * 7 = 5040 or
nPr = 10P4= 5040
To find the number of ways that 4 flags can be displayed on a flagpole, one above the other, if 10 different flags are available, we can use the concept of permutations.
In this case, we need to select 4 flags out of 10 available flags and arrange them in a specific order. Since we are arranging the flags one above the other, the order is important.
The number of ways to select and arrange 4 flags out of 10 can be calculated using the formula for permutations:
nPr = n! / (n-r)!
where n is the total number of objects (10 flags) and r is the number of objects selected (4 flags).
Let's plug in the values:
10P4 = 10! / (10-4)!
= 10! / 6!
Now, let's simplify:
10! = 10 x 9 x 8 x 7 x 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
Substituting these values back into the formula:
10P4 = (10 x 9 x 8 x 7 x 6!) / (6 x 5 x 4 x 3 x 2 x 1)
Canceling out the common factors:
10P4 = 10 x 9 x 8 x 7
= 5,040
Therefore, there are 5,040 different ways that 4 flags can be displayed on a flagpole, one above the other, if 10 different flags are available.
To find the number of ways that 4 flags can be displayed on a flagpole, one above the other, if 10 different flags are available, we can use the concept of permutations.
In this problem, the order of the flags matters because each flag can be displayed in a different position on the flagpole.
To solve this, we can use the formula for permutations of n objects taken r at a time, which is given by:
P(n, r) = n! / (n - r)!
Where "!" denotes the factorial of a number.
In this case, we have 10 different flags available and we need to select 4 flags. Therefore, we can write it as:
P(10, 4) = 10! / (10 - 4)!
Now let's calculate it step by step:
1. Calculate the factorial of 10: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800
2. Calculate the factorial of (10 - 4): (10 - 4)! = 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
3. Divide the result obtained in step 1 by the result obtained in step 2:
P(10, 4) = 3,628,800 / 720 = 5,040
Therefore, there are 5,040 different ways that 4 flags can be displayed on a flagpole, one above the other, if 10 different flags are available.