Question

How do I find n in the the permutation equation of nP3 = 990

Answer 1

Answer:

n=11

Step-by-step explanation:

Permutations

The formula to calculate permutations is:

$\displaystyle nPm=\frac{n!}{(n-m)!}$

We know nP3=990. Substituting:

$\displaystyle nP3=\frac{n!}{(n-3)!}=990$

Expanding the factorial in the numerator:

$\displaystyle \frac{n(n-1)(n-2)(n-3)!}{(n-3)!}=990$

Simplifying:

$n(n-1)(n-2)=990$

This equation can be easily solved by inspection. The product of three consecutive numbers resulting 990. Starting from greatest to smallest, those numbers are 11,10, and 9, thus:

$n(n-1)(n-2)=11*10*9$

It follows that n=11