what is the answer to P(10,10) and why?

Question

college algebra

Answer 1

It sounds like you might be asking about permutations. A permutation is when you are given some number of objects (n) and asked to choose a certain number of them (r), where order matters. You can solve problems involving permutations either by thinking through them logically or by applying the formula for permutations, P(n,r) = n! / (n-r)!.

 

 

HERE'S AN EXAMPLE:

 

10 students are racing in a track and field event. The first, second, and third finishers will be given gold, silver, and bronze medals respectively. How many different ways are there to give out the three medals?

 

That example asks you to choose r = 3 students from n = 10 students, and order matters. If I pick John, George, and Kristen, in that order, then John gets gold, George gets silver, and Kristen gets bronze. But if I reverse the order, I get a different outcome: Kristen gets gold, George gets silver, and John gets bronze.

 

You would write that problem as P(10,3), because you're doing a permutation of 10 students into 3 spots. Think through it logically like this: There are 10 possible students I could pick for the first spot, then 9 remaining who I could pick for the second spot, then 8 remaining who I could pick for the third spot. That means there are a total of 10×9×8 = 720 permutations of students.

 

If you want to use the formula instead, remember that the formula for a permutation is P(n,r) = n! / (n-r)!. In the track and field example, that means you'd have:

 

10! / (10-3)! = 10! / 7! = (10×9×8×7×6×5×4×3×2×1) / (7×6×5×4×3×2×1)

 

Notice that most of the terms cancel each other out (everything in red), so you're left with 10×9×8 = 720 permutations of students, like we calculated before.

 

 

NOW BACK TO YOUR QUESTION...

 

P(10,10) means you're given 10 objects and are asked to choose all 10 of them, where order matters. That means you'll keep picking objects one by one until you've run out, lining them up in order. You can either think through it logically like we did to solve the track and field problem the first time, or you can use the formula for permutations like we did to solve the track and field problem the second time. Here's both methods:

 

If you want to just think through it logically, you'll have 10 objects to choose from for the first spot, then 9 for the next spot, then 8 for the next spot, etc. all the way down to 1. That means there are 10×9×8×7×6×5×4×3×2×1 = 3,628,800 ways to permute the objects.

 

If you want to plug it into the formula, you'll have to know that 0! = 1. Your formula will look like this:

 

P(10,10) = 10! / (10-10)! = (10×9×8×7×6×5×4×3×2×1) / 0! = (10×9×8×7×6×5×4×3×2×1) / 1 = 10×9×8×7×6×5×4×3×2×1 = 3,628,800 ways to permute the objects.

 

Hope this helps!

Answer 2

If you are talking about plotting points on a coordinate system, start from the origin P(0, 0).  Move 10 units to the right from the origin.  Then move 10 units up from the preceding position.  The final position is your point P(10, 10).  This is because any coordinate is in the form P(x, y).  The x-axis moves from left to right direction.  Right, if the x value is positive. The y-axis moves from up to down direction.  Up, if the y value is positive.