nPr=6720 and nCr=56, then the value if r is___?
6720/56 = 120
So, you have nPr = nCr * 5!
That means that r=5.
Review the definitions of nPr and nCr to see why this is so.
To find the value of r, we can use the formula for nPr and nCr.
nPr (permutations) calculates the number of ways to arrange r objects from a total of n objects, while nCr (combinations) calculates the number of ways to choose r objects from a total of n objects without considering their arrangement.
Given:
nPr = 6720
nCr = 56
We can use the relation between nPr and nCr:
nPr = nCr * r!
We can rearrange the formula and solve for r:
r! = nPr / nCr
r! = 6720 / 56
Let's calculate the value of r:
r! = 120
To find the value of r, we need to find the factorial of r that equals 120.
By inspecting the possible values, we can deduce that r = 5 satisfies this condition:
5! = 5 x 4 x 3 x 2 x 1 = 120
So, the value of r is 5.
To find the value of r, we need to use the formulas for permutations (nPr) and combinations (nCr). The given values are nPr = 6720 and nCr = 56.
First, let's find the value of n. To do this, we will solve the equation nPr = 6720.
The formula for permutations is nPr = n! / (n - r)!, where "!" represents the factorial of a number.
In this case, nPr = 6720, so we have the equation:
n! / (n - r)! = 6720
Next, let's find the value of nCr. The formula for combinations is nCr = n! / (r! * (n - r)!).
We are given nCr = 56, so we have the equation:
n! / (r! * (n - r)!) = 56
Now we have a system of two equations:
n! / (n - r)! = 6720 (Equation 1)
n! / (r! * (n - r)!) = 56 (Equation 2)
To solve this system, we can divide equation 1 by equation 2:
((n - r)! * (n - r)!) / (r! * (n - r)!) = 6720/56
Simplifying, we get:
(n - r)! / r! = 120
Since (n - r)! / r! is the same as nCr, the equation becomes:
nCr = 120
We are given that nCr = 56, which is not equal to 120. Therefore, there is no solution for the given values of nPr = 6720 and nCr = 56.