Simplify the expression 6P3.
I don't know how to solve it so if you could help me with it as well i would really appreciate it.
nvm i guessed 120 and got it right
nPr = n! / (n - r)!
So,
6P3 = 6! / (6 - 3)!
6P3 = (6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1)
6P3 = (6 x 5 x 4)
6P3 = 120
Well, 6P3 stands for the permutation of 6 objects taken 3 at a time. To simplify it, you can use the formula for permutations, which is nPr = n! / (n - r)!. In this case, 6P3 is equal to 6! / (6 - 3)!.
Let's break it down step by step:
First, calculate 6! which stands for 6 factorial. It means multiplying 6 by all the positive integers less than it. So, 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.
Next, calculate (6 - 3)! which is equal to 3!. It means multiplying 3 by all the positive integers less than it. So, 3! = 3 x 2 x 1 = 6.
Now, divide 6! by 3! to get the final result: 720 / 6 = 120.
Therefore, 6P3 simplifies to 120.
To simplify the expression 6P3, we can use the permutation formula. The formula for permutations is:
P(n, r) = n! / (n - r)!
In this case, n = 6 and r = 3.
So, substituting these values into the formula:
P(6, 3) = 6! / (6 - 3)!
Now, let's calculate the factorial terms:
6! = 6 x 5 x 4 x 3 x 2 x 1
and
(6 - 3)! = 3! = 3 x 2 x 1
So, the expression becomes:
6P3 = 6! / (6 - 3)! = 6! / 3!
Simplifying further:
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
3! = 3 x 2 x 1 = 6
Now, divide these two values:
6P3 = 720 / 6 = 120
Therefore, 6P3 is equal to 120.
To simplify the expression 6P3, we will first explain what the symbol "P" means in this context. In mathematics, the symbol "P" typically represents "permutation." A permutation is an arrangement of objects in a particular order. In this case, we are dealing with a permutation of selecting 3 objects from a set of 6 objects.
To calculate the value of 6P3, we can use the formula for permutations:
nPr = n! / (n - r)!
where n is the total number of objects and r is the number of objects being selected. "!" represents the factorial function.
In our case, n = 6 and r = 3:
6P3 = 6! / (6 - 3)!
= 6! / 3!
We need to calculate the factorials of both 6 and 3. The factorial of a number is the product of all positive integers less than or equal to that number.
6! = 6 x 5 x 4 x 3 x 2 x 1
3! = 3 x 2 x 1
Now, let's substitute these values into the formula:
6P3 = (6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1)
Performing the calculations, we get:
6P3 = 720 / 6
= 120
Therefore, the simplified expression 6P3 is equal to 120.