What Are the Easiest Methods to Solve nPr=60 for n When r=3?

[zenity]

Was just wondering if there was a "shorter" method of solving this problem.

nPr = 60.

nPr = n!/(n-r)!

n=?
r=3

Works out to be

n(n-1)(n-2) = 60.

From here on, what different options do I have? I have several ways of solving it, but was wondering what would be the "easiest" method.

 

[vincentchan]

since n is integer, find all the factors of 60, which are 2,3,4,5 and see which 3 consecutive numbers satisfy n(n-1)(n-2)=60

 

[thepatientmental]

There are a few different approaches you could take to solve this problem, but the "easiest" method may vary depending on personal preference and comfort with different techniques. Here are a few possible options:

1. Use a calculator or online tool: If you have access to a calculator or an online permutation calculator, you can simply plug in the values of n and r and it will give you the answer (in this case, n=5). This may be the quickest and most straightforward method for some people.

2. Use a formula or equation: As you mentioned, the formula for permutations is nPr = n!/(n-r)!. You can rearrange this to solve for n by multiplying both sides by (n-r)! and then dividing by nPr. In this case, it would look like n = nPr * (n-r)!/r!. This method may take a little bit longer but can be useful if you don't have access to a calculator or if the numbers are more complex.

3. Use a table or chart: Another way to solve permutations is by creating a table or chart to list out all the possible combinations. For this problem, you could list out all the numbers from 1 to 5 and then find all the combinations of 3 numbers from that list. This method may take a bit more time and effort, but it can be helpful for visual learners or those who prefer a hands-on approach.

Ultimately, the "easiest" method may depend on your personal preference and comfort level with different techniques. It's always a good idea to try out a few different methods and see which one works best for you. Keep in mind that practice and familiarity with permutations will also make the process easier over time.